Improving Steering Module Efficiency for Incremental Loading Finite Element Numeric Models

Transcription

1 Brigham Young University BYU ScholarsArchive All Theses and Dissertations Improving Steering Module Efficiency for Incremental Loading Finite Element Numeric Models Ryan L. Kitchen Brigham Young University - Provo Follow this and additional works at: Part of the Civil and Environmental Engineering Commons BYU ScholarsArchive Citation Kitchen, Ryan L., "Improving Steering Module Efficiency for Incremental Loading Finite Element Numeric Models" (2006). All Theses and Dissertations This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact scholarsarchive@byu.edu, ellen_amatangelo@byu.edu.

2 IMPROVING STEERING MODULE EFFICIENCY FOR INCREMENTAL LOADING FINITE ELEMENT NUMERIC MODELS by Ryan L. Kitchen A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Department of Civil and Environmental Engineering Brigham Young University April 2006

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4 Copyright 2006 Ryan L. Kitchen All Rights Reserved

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6 BRIGHAM YOUNG UNIVERSITY GRADUATE COMMITTEE APPROVAL of a thesis submitted by Ryan L. Kitchen This thesis has been read by each member of the following graduate committee and by majority vote has been found to be satisfactory. Date Alan K. Zundel, Chair Date E. James Nelson Date A. Woodruff Miller

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8 BRIGHAM YOUNG UNIVERSITY As chair of the candidate s graduate committee, I have read the thesis of Ryan L. Kitchen in its final form and have found that (1) its format, citations, and bibliographical style are consistent and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the graduate committee and is ready for submission to the university library. Date Alan K. Zundel Chair, Graduate Committee Accepted for the Department E. James Nelson Graduate Coordinator Accepted for the College Alan R. Parkinson Dean, Ira A. Fulton College of Engineering and Technology

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10 ABSTRACT IMPROVING STEERING MODULE EFFICIENCY FOR INCREMENTAL LOADING FINITE ELEMENT NUMERIC MODELS Ryan L. Kitchen Department of Civil and Environmental Engineering Master of Science Engineers frequently use computerized numeric models to calculate and predict water levels and current patterns for rivers, bays, and other bodies of water. This computation often involves an iterative process known as incremental loading that can cause frustration and consume a lot of time. Although the steering module in the Surface-water Modeling System (SMS) automates incremental loading to minimize user interaction, it can still be very time consuming. This thesis examines the steering module and the incremental loading process to improve its efficiency. Specifically, the RMA2 and FESWMS models are utilized. Two methods of improving efficiency are examined. The first includes creating predicted solution files for each step of the incremental loading process. These

11 predictions allow the steering module to take larger steps and decrease the computation time. The second method changes the algorithm used to determine the size of each step. Finally, the interface to the process was examined and simplified to require minimal input and to make the input more intuitive.

12 ACKNOWLEDGMENTS I appreciate Dr. Zundel for hiring me, generously giving his advice, helping in the research, implementing the code, and editing this document. Thanks to my committee for their help in putting together this thesis and to the SMS developers for their coordination and assistance. I also appreciate Janice Sorenson for checking the formatting of this thesis and her care to help me graduate. Thanks to the Utah Department of Transportation for funding the Capitol Reef oxbow restoration project used as a test case in this thesis. Finally, I am deeply thankful for my family, especially my wife, Mardie Jo, for her extraordinary support and patience.

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14 TABLE OF CONTENTS LIST OF TABLES...ix LIST OF FIGURES...xi 1 Introduction Background Research Objectives Hydraulic Trends Identifying Trends Applying Trends Implementing Spindown Predictions Creating Predicted Hotstart Files Choosing the Best Spindown Prediction Method Results The Spindown Step Size Step Size Changes Minimizing Delays Results Recommendations to Best Utilize the Steering Module Initial Condition and Minimum Value Percentages Steering Combination Recommendations Final Results vii

15 7 Conclusion Summary Future Work References viii

16 LIST OF TABLES Table 3-1: Files Used for Predictions...36 Table 3-2: Prediction Results for FESWMS Simple Channel Flume...39 Table 3-3: Prediction Results for Capitol Reef...41 Table 3-4: Best Prediction Methods...43 Table 3-5: RMA2 Simple Channel Flume Results with Predictions...46 Table 3-6: FESWMS Simple Channel Flume Results with Predictions...48 Table 3-7: RMA2 Tributary Results with Predictions...49 Table 3-8: FESWMS Capitol Reef Results with Predictions...51 Table 4-1: Procedure for Decreasing Sizes of Failed Steps...54 Table 4-2: Quick Rebound Example of the New Spindown Method...55 Table 4-3: Slow Rebound Example of the Old Spindown Method...55 Table 4-4: Using the Maximum Step Size...56 Table 4-5: RMA2 Simple Channel Flume Results with New Steps...59 Table 4-6: FESWMS Simple Channel Flume Results with New Steps...61 Table 4-7: RMA2 Tributary Results with New Steps...63 Table 4-8: FESWMS Capitol Reef Results with New Steps...64 Table 5-1: Initial Conditions...73 Table 5-2: Recommendations for Which Steering Mode to Use...76 ix

17 Table 6-1: RMA2 Simple Channel Flume Results After Thesis...80 Table 6-2: FESWMS Simple Channel Flume Results After Thesis...81 Table 6-3: RMA2 Tributary Results After Thesis...83 Table 6-4: FESWMS Capitol Reef Results After Thesis...84 x

18 LIST OF FIGURES Figure 1-1: Two-Dimensional Finite Element Mesh Example...2 Figure 1-2: Initial Condition...4 Figure 1-3: WSE Spindown Process...6 Figure 1-4: The Original Steering Dialog...8 Figure 2-1: Location of Nodes in Simple Flume Used to Identify Trends...14 Figure 2-2: Vx Trend with Geometry Steering for Simple Flume...15 Figure 2-3: Vy Trend with Geometry Steering for Simple Flume...15 Figure 2-4: WSE Trend with Geometry Steering for Simple Flume...16 Figure 2-5: Vx Trend with WSE Steering for Simple Flume...17 Figure 2-6: Vy Trend with WSE Steering for Simple Flume...17 Figure 2-7: WSE Trend with WSE Steering for Simple Flume...18 Figure 2-8: Vx Trend with Geometry and WSE Steering for Simple Flume...19 Figure 2-9: Vy Trend with Geometry and WSE Steering for Simple Flume...20 Figure 2-10: WSE Trend with Geometry and WSE Steering for Simple Flume...20 Figure 2-11: Location of Nodes in Capitol Reef Used to Identify Trends...22 Figure 2-12: Vx Trend with Geometry Steering for Capitol Reef...22 Figure 2-13: Vy Trend with Geometry Steering for Capitol Reef...23 Figure 2-14: WSE Trend with Geometry Steering for Capitol Reef...23 Figure 2-15: Vx Trend with WSE Steering for Capitol Reef...24 xi

19 Figure 2-16: Vy Trend with WSE Steering for Capitol Reef...25 Figure 2-17: WSE Trend with WSE Steering for Capitol Reef...25 Figure 2-18: Vx Trend with Geometry and WSE Steering for Capitol Reef...26 Figure 2-19: Vy Trend with Geometry and WSE Steering for Capitol Reef...27 Figure 2-20: WSE Trend with Geometry and WSE Steering for Capitol Reef...27 Figure 2-21: Linear Predictions...29 Figure 2-22: Quadratic Predictions...31 Figure 2-23: Accuracy and Improvement of Linear and Quadratic Predictions...31 Figure 2-24: Error in Linear and Quadratic Predictions when Steering on WSE...32 Figure 3-1: The Simple Channel Flume Model...39 Figure 3-2: The Capitol Reef Model...41 Figure 3-3: RMA2 Simple Channel Flume Results with Predictions...46 Figure 3-4: FESWMS Simple Channel Flume Results with Predictions...48 Figure 3-5: RMA2 Tributary Results with Predictions...50 Figure 3-6: FESWMS Capitol Reef Results with Predictions...51 Figure 4-1: RMA2 Simple Channel Flume Results with New Steps...60 Figure 4-2: FESWMS Simple Channel Flume Results with New Steps...62 Figure 4-3: RMA2 Tributary Results with New Steps...63 Figure 4-4: FESWMS Capitol Reef Results with New Steps...65 Figure 5-1: Old Steering Dialog...68 Figure 5-2: New Steering Dialog...68 Figure 5-3: Multiple Head Boundary Conditions Example...74 Figure 6-1: RMA2 Simple Channel Flume Results After Thesis...80 xii

20 Figure 6-2: FESWMS Simple Channel Flume Results After Thesis...82 Figure 6-3: RMA2 Tributary Results After Thesis...83 Figure 6-4: FESWMS Capitol Reef Results After Thesis...85 xiii

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22 1 Introduction Hydraulic numeric models compute parameters such as water levels and current patterns for rivers, bays, and other bodies of water. This computation often involves an iterative process that can cause frustration and consume a lot of time. This research report describes the testing of various applications of two numeric models to better understand the process and automate portions to make the computation process faster and easier. 1.1 Background A numeric model consists of a two-dimensional grid of nodes and elements that represents the actual body of water being modeled as shown in Figure 1-1. This example of a two-dimensional finite element network or mesh displays elements as triangles and nodes as points at the middle and ends of each side of each triangle. Elements may also be shaped in the form of a trapezoid and nodes may be located in the center of these elements. Values are associated with the nodes outlined (such as ground elevation, water surface elevation, and velocity magnitude). Users input the ground elevation under the water (bathymetry) and the numeric model outputs the water surface elevation, velocity, and other hydraulic parameters. 1

23 Figure 1-1: Two-Dimensional Finite Element Mesh Example The Surface-water Modeling System (SMS) software package eases the creation and calibration of numeric models with the use of a graphical display. SMS shows the location of the nodes and elements and can generate contours based on the values at each node. Figure 1-1 illustrates color-filled or continuous contours based on the bathymetry elevation at each node. The graphical display allows intuitive creation and modification of the nodes and elements of the two-dimensional finite element mesh. SMS also helps in assigning roughness, viscosity, flow rate, water surface elevation, and other input parameters. The flow rate coming into the boundary of the mesh and the water surface elevation at the exiting boundary of the mesh represent the boundary conditions. The boundary conditions should reflect the actual flow rate and water surface elevation of the water that the model simulates. The mesh in Figure 1-1 consists of two inflow boundary conditions at the left side of the picture 2

24 and one water surface elevation (head) boundary condition at the right side of the picture. This research applies two numerical modeling engines, the United States Army Corps of Engineers (USACE) RMA2 package version 4.5 (USACE 2005) and the Federal Highway Administration s (FHWA) FESWMS version (Froehlich 2003). Both of these engines compute the velocity in the x-direction and y-direction and the water surface elevation for each node within the mesh. The following section describes the input required for these models Initial Conditions Input for RMA2 and FESWMS includes the initial conditions of a water surface elevation and a velocity vector value at each node (Froehlich 1996). The mesh shown in Figure 1-1 consists of 2,075 elements and 4,400 nodes. Therefore, a complete set of initial conditions includes 13,200 values (3 values * 4,400 nodes). Manual specification of this many values would be drudging even if the user had a valid idea of what they are. Instead, coldstart conditions set the water surface elevation at a constant level for all nodes (generally at the same level as the water surface elevation boundary condition) and the velocity vector magnitudes to zero. RMA2 and FESWMS use the principles of conservation of mass and conservation of momentum to calculate flow parameters for a given numeric simulation (Lee and Froehlich 1986). First the model takes the initial condition values for each node and computes how far out of balance the system is. It then adjusts the estimates for these values for each node to more closely conserve mass and 3

25 momentum. These new values become the basis for another iteration as the model again adjusts these values. The engines repeat this process until the values converge or diverge past a given limit. In a stable model, these values converge and the engines find velocities and water levels that result in balance of momentum and mass. In an unstable model, these values diverge or oscillate, resulting in no valid solution. In any realistic situation, when the user sets the initial condition with the velocity magnitudes to zero and the water level equal to the water surface elevation boundary condition, the water level does not submerge the upper nodes of the model because of the slope of the ground surface. Figure 1-2 shows an example of a long domain where setting the initial condition water level to the boundary condition leaves nodes in the upper section of the model dry. This causes instability and RMA2 and FESWMS generally fail, especially if entire cross sections are dry. Dry cross sections prevent water from flowing through the inflow boundary. Obviously, no flow solution can be found if the channel dries out completely. Figure 1-2: Initial Condition As a solution, the user may increase the water level to submerge all nodes. This prevents drying of the channel. However, it also increases the size of the change 4

26 required to match specified conditions and the actual condition where the water exits at the boundary condition water level. A large difference will most likely cause RMA2 and FESWMS to fail (Froehlich 1996). If no stable coldstart value exists, the user must create a nontrivial set of initial conditions. The next section describes a process which attempts to create these values Incremental Loading or the Spindown Process The incremental loading or spindown process involves modifying both the initial condition and boundary conditions from desired values to create a stable coldstart condition. Then the process uses the solution from this modified starting condition as the initial condition or hotstart condition for another simulation that more closely approximates the final value. The user then repeats this process of using the previous solution to step closer to the final value until the model reaches the final value. Figure 1-3 shows an example of how the spindown process works. Say the outflow boundary condition lies 5,070 feet above sea level, but to create a situation that can converge from coldstart, the initial water surface elevation and the boundary condition must be set to 5,135 feet above sea level. These conditions result in a solution that has water moving through the system, but with the wrong boundary conditions (first frame of Figure 1-3). However, the solution is closer to the desired conditions than the coldstart. If the user then changes the modified simulation s boundary conditions from 5,135 feet to 5,122 feet, the model may use the solution from the 5,135-foot water surface elevation as hotstart initial values, resulting in a 5

27 solution to conditions closer to the desired values (5,122 feet instead of 5,135 feet as shown in the second frame of Figure 1-3). The user then repeats this process of lowering boundary conditions and rerunning the model to arrive at a solution with a 5,070-foot water surface elevation boundary condition, which is the desired level (sixth frame of Figure 1-3). This may require several steps to go from the initial condition to the actual condition. This process is known as spinning down the water surface elevation. Solution to coldstart condition (5,135 feet). Solution to 5,122-foot boundary condition. Solution to 5,110-foot boundary condition. Solution to 5,095-foot boundary condition. Solution to 5,080-foot boundary condition. Final solution to desired 5,070-foot boundary condition. Figure 1-3: WSE Spindown Process 6

28 Another possible mode of incremental loading consists of flattening the bathymetry to create a stable model without raising the water level, and then stepping the bathymetry up to the actual level in a process known as spinning up the geometry. Two other incremental loading processes that add model stability include spinning down the eddy viscosity and spinning up the flow rates. In reality, the user may alter any model property to add stability to the model during incremental loading. Additionally, the user may employ a single incremental loading process or combine methods to more than one parameter simultaneously such as spinning on both eddy viscosity and geometry. The incremental loading process makes solving a complex, but realistic model possible, but at the same time requires a great deal of user interaction. These simulations may also be confusing, frustrating, and very time consuming. SMS has attempted to automate the process through its steering module Steering Automating the Spindown Process The SMS steering module, created by Tom Moreland (Moreland), automates the spindown process. This feature is accessed by selecting Data Steering Module on the SMS Menu Bar. The original steering module required the user to specify initial values for each parameter being loaded as shown in Figure 1-4. However, a single parameter could control multiple locations in the model. For instance, loading water surface elevation affects the water level at all outflow boundaries. Therefore, the initial value for steering consisted of a percentage of the desired value rather than the actual value. For example, in a model of the Fremont River in Capitol Reef National 7

29 Park, the desired boundary water surface elevation is 5,070 feet. However, the model required an initial boundary condition water level of 5,135 feet in order for the model to run. Therefore, the initial condition was set to % of the desired water surface elevation (5,135 / 5,070), which corresponded to a water level of 5,135 feet. Figure 1-4: The Original Steering Dialog The original method also required the specification of a minimum allowable step before it would stop the spindown process. It then performed the following four steps: 1. Alter the specified model to create a temporary model using the initial percentage values. 2. Invoke the desired numeric engine to solve the temporary model. 8

30 3. Modify incremental loading parameters, bringing the temporary model closer to the specified model. 4. Rerun the model using the solution of the previous run as the initial conditions. 5. Repeat steps 3-4 until it finishes or the minimum step is reached. 1.2 Research Objectives Specification of initial values as percentages and minimum step sizes has been confusing to users. In addition, applying a single percentage is problematic and unstable. The steering process can also be very time-consuming requiring many model runs. With this in mind, this thesis has three main objectives: 1. Research trends in hydraulic parameters during the spindown process to explore the possibility of predicting solutions to decrease the computation time. 2. Test different algorithms for determining spindown step sizes (optimizing step 3 of the steering process). 3. Give recommendations to best utilize the steering module. The following sections explain how these objectives may be accomplished Hydraulic Trends and Predicted Solutions This research analyzes trends that occur in the velocity and water surface elevation values for specific nodes during the spindown process. Identifying these trends facilitates the definition of a prediction algorithm. After a couple steps of the spindown process, this algorithm predicts the velocity and water surface elevation 9

31 values for the next step based on the values from previous steps. Applying this algorithm for all nodes of the model results in a hotstart file based on these predicted values. Since the predicted hotstart file represents the specified model better than the hotstart file from the previous step, the model can then take larger steps. If the model takes fewer but larger steps, then it will decrease the spindown computation time The Spindown Step Size Another variable in the spindown process is the step size or adjustment made to model parameters. Small steps increase the stability, but also increase the number of runs and computation time. Therefore, optimization of the step size occurs when each step becomes as large as possible without causing the run to fail. Since each step includes several iterations while the model tries to balance momentum and mass, decreasing the number of iterations in each step also improves spindown efficiency. This research experiments with different spindown step size algorithms to decrease the number of steps and the number of iterations per step Recommendations to Best Utilize the Steering Module Previous versions of the steering module confused users. Concerns included how to choose the initial values and the minimum steps required by the steering dialog as shown in Figure 1-4, and what these values meant. This research simplifies the steering input by eliminating the need to enter the initial values and minimum step sizes. These variables receive recommended default values to avoid confusion and bad values. However, the user still has the option to override the initial values. This 10

32 thesis also gives recommendations for which steering combination to use for different types of models based on the results of this research Test Cases This research utilizes four different test cases. The Simple Flume consists of a basic flume with little turbulence and subcritical flow and applies to FESWMS. It simulates 1,000 cfs running through a 2,500-foot wide and 50,000-foot long channel with a downstream water surface elevation of ft. Results assist in understanding general trends in hydraulic parameters during the spindown process. The simplicity and lack of instabilities in this model allows for continuous trends and provides results for a simple model. Similar to the first test case, the Simple Flume with a channel also consists of a basic flume with little turbulence and subcritical flow. However it adds a channel to represent a simple but more realistic model. The Simple Channel Flume simulates 1,200,000 cfs running through a 10,000-foot wide and 100,000-foot long channel with a downstream water surface elevation of 16 feet. It applies to both RMA2 and FESWMS and provides an illustration of improvements for a realistic simple model during this research. The final two test cases, Tributary for RMA2 and Capitol Reef for FESWMS, illustrate the behaviors of hydraulic parameters during the spindown process for more realistic conditions. The Tributary case simulates 55,000 cfs running through its main channel and 600 cfs coming from a tributary and has a downstream water surface elevation of 33 feet. Capitol Reef simulates 6,551 cfs (representing a 11

33 50-year flood) and has a downstream water surface elevation of 5,070 feet. Improvements in the computation time of these test cases indicate how successful this research could be for other similar models. 12

34 2 Hydraulic Trends This chapter explores the possibility of creating predicted solutions by better understanding the trends that occur during the spindown process. As the water surface elevation, geometry, flow rate, and eddy viscosity change, trends in the hydraulic parameters at each node often exist. Identifying and understanding these trends can help in the development of algorithms to predict solutions for boundary conditions later in the steering process. Using accurate predictions as hotstart files during incremental loading results in fewer required steps in the process and fewer iterations per step, thus saving considerable computation time. The following sections describe the methodology used to identify hydraulic trends, illustrate the patterns found for different loading combinations, and document the application of these trends in determining the best prediction methods to use for the steering module. 2.1 Identifying Trends In order for the creation of predicted hotstart files in the steering module to work well, a trend has to exist that relates velocity vectors and water surface elevation with spindown percentages. For this reason, several tests were conducted to ensure that each hydraulic parameter for each loading combination will produce some type of trend. The figures shown in this section illustrate the trends in hydraulic parameters 13

35 during the spindown process for two of the test cases. The first test case, Simple Flume, produced basic trends with subcritical flow and very little turbulence to get an idea of what type of trends exist. The second test case, Capitol Reef, represents a realistic situation, and verifies that the basic trends observed in the Simple Flume continue in a more complex model Simple Flume Trends This research selected a sample of five nodes throughout the Simple Flume model to evaluate the velocities and water surface elevation for each step of the spindown process. Figure 2-1 shows the locations of the selected nodes. Plotting the velocity value or water surface elevation on the y-axis and the corresponding spindown percentage on the x-axis for each run allows for visual evaluation of trends. Figure 2-2, Figure 2-3, and Figure 2-4 present the nodal trends for the velocity in the x-direction (Vx), the velocity in the y-direction (Vy), and the water surface elevation (WSE) respectively for geometric steering. Figure 2-1: Location of Nodes in Simple Flume Used to Identify Trends 14

36 Geometry Steering Vx Trend Velocity (ft/s) Percent of Target Geometry Node 29 Node 121 Node 172 Node 277 Node 383 Figure 2-2: Vx Trend with Geometry Steering for Simple Flume Geometry Steering Vy Trend Velocity (ft/s) Percent of Target Geometry Node 29 Node 121 Node 172 Node 277 Node 383 Figure 2-3: Vy Trend with Geometry Steering for Simple Flume 15

37 Geometry Steering WSE Trend WSE (ft) Percent of Target Geometry Node 29 Node 121 Node 172 Node 277 Node 383 Figure 2-4: WSE Trend with Geometry Steering for Simple Flume These figures illustrate that steering on geometry results in somewhat of a curvilinear trend for Vx and nearly a linear trend for WSE. The simplicity of the model eliminates Vy making the trend in Vy useless. A quadratic equation may work the best in predicting Vx, but a linear equation may also adequately describe the trend for smaller steps. A linear trend is appropriate for predicting WSE. In a model with flow in both directions, the Vy trend should appear similar to the Vx trend. Most importantly, no sharp changes in the slope exist with any of the curves for the three figures when steering on geometry. The next set of figures (Figure 2-5, Figure 2-6, and Figure 2-7) show the trends when steering on water surface elevation. 16

38 WSE Steering Vx Trend Velocity (ft/s) Percent of Target WSE Node 29 Node 121 Node 172 Node 277 Node 383 Figure 2-5: Vx Trend with WSE Steering for Simple Flume WSE Steering Vy Trend Velocity (ft/s) Percent of Target WSE Node 29 Node 121 Node 172 Node 277 Node 383 Figure 2-6: Vy Trend with WSE Steering for Simple Flume 17

39 WSE Steering WSE Trend WSE (ft) Percent of Target WSE Node 29 Node 121 Node 172 Node 277 Node 383 Figure 2-7: WSE Trend with WSE Steering for Simple Flume These figures contain inconsistent curves. Linear and quadratic equations may represent parts of each trend, but sharp breaks exist in the curves when the water surface elevation approaches its final value for each node. This is especially noticeable for the WSE trend. The trends in Vx show how the velocity increases as the water surface elevation decreases. After the water surface elevation reaches its final value for each node, the velocity levels off to a stable value. This produces an S shaped curve. Interestingly, the model overshot most of the nodes final values at the end of the S- curve. Nearby nodes arriving at their final values at the same time may cause a slight instability in the area. Otherwise, the cause for this is unknown. 18

40 These inconsistencies mean that finding a single equation that defines each curve and generating a simple method to predict future values in the spindown process is unlikely. Cubic equations may represent the velocity values but not the water surface elevation. Therefore, the issue becomes trying to find an algorithm that can predict when the sharp change in slope for each node will occur. Linear or quadratic equations could then represent the curves before and after the sharp change in slope. The final set of figures (Figure 2-8, Figure 2-9, and Figure 2-10) show the trends discovered when steering on geometry and water surface elevation jointly. Geometry and WSE Steering Vx Trend Velocity (ft/s) Percent of Target WSE Percent of Target Geometry Node 29 Node 121 Node 172 Node 277 Node 383 Figure 2-8: Vx Trend with Geometry and WSE Steering for Simple Flume 19

41 Geometry and WSE Steering Vy Trend Velocity (ft/s) Percent of Target WSE Percent of Target Geometry Node 29 Node 121 Node 172 Node 277 Node Figure 2-9: Vy Trend with Geometry and WSE Steering for Simple Flume Geometry and WSE Steering WSE Trend WSE (ft) Percent of Target WSE Percent of Target Geometry Node 29 Node 121 Node 172 Node 277 Node 383 Figure 2-10: WSE Trend with Geometry and WSE Steering for Simple Flume 20

42 These figures nearly reproduce the results shown by steering on water surface elevation alone. However, the curves do not change slope as abruptly, and the Vx and WSE values continue to change even after the water surface elevation reaches the ground elevation because the geometry continues to change until the model completely spins down. Once again, the inconsistencies present the need to find an algorithm to predict when the changes in slope will occur. Linear or quadratic equations could then represent the curves before and after the sharp change in slope Capitol Reef Trends The next test uses the more realistic Fremont River model located in Capitol Reef National Park. This test also used a sample of five nodes throughout the Capitol Reef model to affirm the validity of the previous results. This more realistic model introduces changing slopes and supercritical flow. Figure 2-11 shows the network and the locations of the observation nodes used to evaluate the trends. Figure 2-12, Figure 2-13, and Figure 2-14, show the trends when spinning on geometry for Vx, Vy, and WSE respectively. 21

43 Figure 2-11: Location of Nodes in Capitol Reef Used to Identify Trends Geometry Steering Vx Trend 8 6 Velocity (ft/s) Percent of Target Geometry Node 600 Node 1500 Node 2300 Node 3000 Node 3700 Figure 2-12: Vx Trend with Geometry Steering for Capitol Reef 22

44 Geometry Steering Vy Trend Velocity (ft/s) Percent of Target Geometry Node 600 Node 1500 Node 2300 Node 3000 Node 3700 Figure 2-13: Vy Trend with Geometry Steering for Capitol Reef Geometry Steering WSE Trend WSE (ft) Percent of Target Geometry Node 600 Node 1500 Node 2300 Node 3000 Node 3700 Figure 2-14: WSE Trend with Geometry Steering for Capitol Reef 23

45 These figures illustrate that steering on geometry presents a linear trend for WSE. The Vx and Vy curves show that a quadratic or linear equation could be used to approximate activity in general except node 1500 tends to follow a more erratic trend. This is because node 1500 is located in an area of high instability where wetting and drying and jumps between subcritical and supercritical flow occur frequently during the spindown process. Most importantly, with the exception of areas of instability, no sharp changes in the slope exist with any of the curves for the three figures when steering on geometry. This reaffirms the trends observed in the Simple Flume. The next set of figures (Figure 2-15, Figure 2-16, and Figure 2-17) show the trends discovered when steering on water surface elevation. WSE Steering Vx Trend 8 6 Velocity (ft/s) Percent of Target WSE Node 600 Node 1500 Node 2300 Node 3000 Node 3700 Figure 2-15: Vx Trend with WSE Steering for Capitol Reef 24

46 WSE Steering Vy Trend 6 5 Velocity (ft/s) Percent of Target WSE Node 600 Node 1500 Node 2300 Node 3000 Node 3700 Figure 2-16: Vy Trend with WSE Steering for Capitol Reef WSE Steering WSE Trend WSE (ft) Percent of Target WSE Node 600 Node 1500 Node 2300 Node 3000 Node 3700 Figure 2-17: WSE Trend with WSE Steering for Capitol Reef 25

47 These figures also reaffirm the trends found in the Simple Flume when steering on water surface elevation. The trends have discontinuous sections of linear and quadratic trends, but also exhibit a sharp break for each node when the water surface elevation approaches that particular node s elevation. The velocity plots also display S-curves, except the Capitol Reef model introduces more variation and negative values. The final set of figures (Figure 2-18, Figure 2-19, and Figure 2-20) show the trends discovered when steering on geometry and water surface elevation jointly. Geometry and WSE Steering Vx Trend Percent of Target WSE Velocity (ft/s) Percent of Target Geometry Node 600 Node 1500 Node 2300 Node 3000 Node 3700 Figure 2-18: Vx Trend with Geometry and WSE Steering for Capitol Reef 26

48 Geometry and WSE Steering Vy Trend Percent of Target WSE Velocity (ft/s) Percent of Target Geometry Node 600 Node 1500 Node 2300 Node 3000 Node 3700 Figure 2-19: Vy Trend with Geometry and WSE Steering for Capitol Reef Geometry and WSE Steering WSE Trend WSE (ft) Percent of Target WSE Percent of Target Geometry Node 600 Node 1500 Node 2300 Node 3000 Node 3700 Figure 2-20: WSE Trend with Geometry and WSE Steering for Capitol Reef 27

49 Once again these figures reproduce the results of the Simple Flume when steering on water surface elevation and geometry. The trends change slope when the water surface elevation approaches a particular node, and the plots continue to curve after the change in slope due to the changing geometry. Additional testing reveals that these same patterns for the different combinations of steering strategies hold true for test cases in RMA Applying Trends The application of linear or quadratic equations for predicting solutions shows promise for steering on geometry. The trends when steering on water surface elevation illustrate the need to create an algorithm to estimate when the sharp change in slope for each node will occur. The following sections define the linear and quadratic equations used to create predictions and a possible method to create predictions when steering on water surface elevation Predictions from Linear Equations The first method to predict a solution involves linear extrapolation. The three hydraulic parameters that make up a solution file, Vx, Vy, and WSE, are projected for each node by finding a rate of change between these parameters and the percentage that the model has spun down. SMS may then predict how much each parameter will change with the next spindown percentage and build a solution file accordingly. Equation 2.1 shows the general equation used to predict each hydraulic parameter for every node in a model. The letter V represents the parameter that the equation is being applied to (Vx, Vy, or WSE), P represents the spindown percentage, and the 28

50 subscripts 1, 2, and p represent values from the first, second, and predicted solution files (the second is the most recent). In the case that the predicted water surface elevation results in a negative water depth, SMS writes the average of the water surface elevation from the most recent solution and the ground elevation. This holds true for all prediction methods. The illustration in Figure 2-21 summarizes the linear prediction method. V p V 21 ( Pp 1) V1 (2.1) P21 Figure 2-21: Linear Predictions 29

51 2.2.2 Predictions from Quadratic Equations The next method to predict a solution file involves quadratic predictions. This method fits a quadratic curve through the previous three values and uses this curve to project to the percentage of the next step. Equation 2.2 shows the general equation for quadratic predictions for the hydraulic parameters. This equation fits a parabolic shape through the previous three solutions to predict the value of the next run. Once again the letter V represents the parameter that the equation is being applied to, P represents the spindown percentage, and the subscripts 1, 2, 3, and p represent values from the first, second, third, and predicted solution files (the third is the most recent). Figure 2-22 illustrates this prediction method. Vp V31 V21 2 V31 P31 V 21 ( P 1) p ( Pp1 ) V1 P31( P31 P21) P21( P31 P21) P31 2 P31 P31(1 ) P21 (1 ) P21 P 21 (2.2) Figure 2-23 shows the water surface elevation trend for node 2,300 of the Capitol Reef model when steering on geometry. It also shows the accuracy and improvement of linear and quadratic predictions compared to using no prediction method. The plot on the right represents a blown up version of the zoom window in the plot on the left. The linear prediction shows considerable improvement over not using any prediction, and the quadratic prediction lies even closer to the actual value. In most cases a quadratic equation will predict better than a linear equation except when the curve changes directions such as in an S-curve. 30

52 Figure 2-22: Quadratic Predictions Geometry Steering WSE Trend Geometry Steering WSE Trend WSE (ft) 5085 WSE (ft) Zoom Window Percent of Geometry Percent of Geometry Node 2300 Quadratic Prediction Linear Prediction No Prediction Node 2300 Quadratic Prediction Linear Prediction No Prediction Figure 2-23: Accuracy and Improvement of Linear and Quadratic Predictions 31

53 2.2.3 Predictions with Water Surface Elevation Steering Figure 2-24 shows the water surface elevation trend for node 2,300 of the Capitol Reef model when steering on water surface elevation. Linear and quadratic equations may accurately predict this trend until it reaches the sharp break in slope. At this point, the model would do better using no prediction method. This demonstrates the need for a different prediction method when steering on water surface elevation. WSE Steering WSE Trend WSE Steering WSE Trend WSE (ft) 5120 WSE (ft) Zoom Window Percent of Target WSE Percent of Target WSE Node 2300 Linear Prediction Node 2300 Linear Prediction Quadratic Prediction No Prediction Quadratic Prediction No Prediction Figure 2-24: Error in Linear and Quadratic Predictions when Steering on WSE If SMS could predict the spindown percentage when the decreasing water surface elevation begins to affect each node, then it could apply an algorithm to create a predicted solution file. The algorithm would use two different linear or quadratic equations to model the slope before and after the falling water surface elevation affects 32

54 each node in the model. The water surface elevation before the break appears perfectly linear since the water surface elevation at each node follows the boundary water surface elevation and a linear (constant) equation could estimate the trend after. For velocity, a linear or quadratic prediction before the break and a constant value after may provide the best results. In order to predict when the slope change will occur for a given node, this research used a method to analyze its neighboring nodes. If any of the neighbor nodes have already reached the break, then the selected node will soon reach the break as well. The following paragraph explains how this is done. After each steering run, each node obtains a percent affected value based on Equation 2.3. This value remains at 100% (the dropping water surface elevation completely affects the node s water surface elevation and velocity) until each node reaches its ultimate water surface elevation and velocity at which this value approaches 0% (the dropping water surface elevation no longer affects the node s water surface elevation and velocity). A predicted percent affected is then calculated for the next run for each node by analyzing the percent affected values of its neighboring nodes according to Equation 2.4. Equation 2.5 and Equation 2.6 show how the predicted percent affected applies to linear and quadratic equations respectively to create wave effect predictions. In these equations, BC WSE represents the boundary condition water surface elevation, N represents the number of neighbor nodes, V represents the parameter that the equation is being applied to, P represents the spindown percentage, the subscripts 1, 2, and p represent values from the first, 33

55 second, and predicted solution files, and PA n represents the percent affected value from each neighbor node. PA 1 2 (2.3) P BC 1 WSE WSE P WSE BC WSE PAn PPA 0.8 PA 0. 2 (2.4) N V p Ax * PPA B (2.5) V p 2 2 Ax * PPA Bx * PPA C (2.6) SMS normalizes the span of predicted percent affected values so that the lowest value is zero and the highest value is one. This helps compensate for the variability in the number of nodes and size of each simulation SMS may use combinations of these prediction methods to better represent the trends. Anytime one of these methods predicts a water surface elevation less than the ground elevation for a given node, it sets the predicted water surface elevation to the node s ground elevation plus half its water depth from the previous run to avoid model instabilities due to drying. 34

56 3 Implementing Spindown Predictions This chapter discusses the application of the knowledge presented in the previous chapter. This involved implementing the most efficient prediction method into the spindown process. The possible methods include linear, quadratic, a mix of linear and quadratic, and wave effect predictions. The mix uses linear predictions for water surface elevation and quadratic predictions for the velocity vectors. Each method works differently depending on which loading combination SMS runs and the model definition (RMA2 or FESWMS). 3.1 Creating Predicted Hotstart Files While steering, RMA2 creates a hotstart file for each run with the name steer#.hot where # represents the steering run number performed. SMS saves these files until it can begin creating predicted hotstart files. Linear and wave effect predictions require two hotstart files written by RMA2 and quadratic predictions require three. Once SMS has enough files to create predictions, it can delete the oldest files as RMA2 creates new hotstart files. SMS names the predicted files prediction#.hot where # represents the steering run number about to be performed. Similar to RMA2, FESWMS creates a solution file for each steering run called steer#.flo where # represents the steering run number performed. SMS uses two or 35

57 three of these solution files to create predicted hotstart files with the name steer#.ini where # represents the steering run number about to be performed. Table 3-1 gives an example of which files SMS may use for a given test case. In the case of linear predictions, SMS needs two solution files from previous runs to create a predicted hotstart file. If the first two successful steering runs were the first and fifth, then SMS could use these two solutions to create a predicted hotstart file for the sixth steering run. SMS names the predicted file prediction6.hot if it uses RMA2 or steer6.ini if it uses FESWMS. The sixth steering run can then use this predicted file instead of the hotstart or solution file from the previous run as input into RMA2 or FESWMS. As these predicted files better represent the final solution, SMS can take larger steps and/or use fewer iterations to converge, and thus spindown more efficiently. Table 3-1: Files Used for Predictions Linear Predictions Quadratic Predictions Model RMA2 FESWMS RMA2 FESWMS First Solution File steer1.hot steer1.flo steer1.hot steer1.flo Second Solution File steer5.hot steer5.flo steer5.hot steer5.flo Third Solution File steer6.hot steer6.flo Predicted Hotstart File prediction6.hot prediction6.flo prediction7.hot prediction7.flo In the case of quadratic predictions, SMS needs three solution files from previous runs to create a predicted hotstart file. If the first three successful steering runs were the first, fifth, and sixth, then SMS could use these three solutions to create 36

58 a predicted hotstart file for the seventh steering run. Once SMS obtains a new solution file, it may then delete the oldest solution file not being used for predictions unless the user specifies to save all files RMA2 RMA2 uses geometry and hotstart files in a specific binary format (USACE 2005). Therefore, SMS has to call another program in order to create a predicted hotstart file from previous hotstart files. The Army Corp of Engineers developed a program in FORTRAN called R2HotFix. The original source code for this program takes two binary geometry files representing the original and altered geometry and the hotstart file from the original geometry to create a new hotstart file for the altered geometry. The binary files come from running a program called gfgen version 4.5 (USACE 2005), which saves the mesh geometry into a binary format. When steering on geometry, gfgen runs before each step because of the changing bathymetry. In part, this research modified the R2HotFix code to take the last two binary geometry files for linear predictions or the last three geometry files for quadratic predictions and their accompanying hotstart files to create a predicted hotstart file. This program may skip the code to read the binary geometry files if the user is not steering on geometry. However, it does not have the capability to create wave effect predictions due to the difficulty of manipulating the R2HotFix program in this manner FESWMS To create predicted hotstart files in FESWMS, SMS uses the last two good.flo solution files for linear or wave effect predictions or the last three good.flo files for 37

59 quadratic predictions to create an.ini hotstart file for the next steering run. The.flo files are in ascii format and contain a heading and four columns for the node numbers, the two directional velocity vector values, and the water surface elevations in the solution set (Froehlich 2002). SMS extracts this information node by node, predicts new values for each node, and creates an.ini hotstart file with the same format as the solution files. 3.2 Choosing the Best Spindown Prediction Method The prediction theory observed in chapter 2 suggests four possible prediction methods to spin down a simulation. These prediction methods include linear, quadratic, mixed (linear and quadratic), and wave effect predictions. In order to choose the best prediction method for each steering combination, the theory was implemented into SMS. The steering module in SMS attempted to spin down two different models using several different steering combinations with each type of prediction method proposed. These results provided sufficient information to determine which prediction method (if any) was best for each steering combination. The first test consisted of spinning down the FESWMS Simple Channel Flume shown in Figure 3-1. Its shape is similar to the Simple Flume, but it is larger, has different boundary conditions, and it has a channel in the middle. Table 3-2 displays the results of spinning down this model for all prediction methods. The rows in each table represent the loading combination used. Geo stands for spinning on geometry, WSE stands for spinning on water surface elevation, Eddy stands for spinning on eddy viscosity, and Flow stands for spinning on flow rate. The columns represent 38

60 the total time of the simulation in minutes and seconds and the total number of runs to spin down the model for each prediction method. This research used a Pentium(R) 4 CPU, 2.40 GHz, and 512 MB of RAM computer and found the spindown times from the time shown on the last run in the SteeringStatus.txt file. Since each prediction method should result in the same solution, the primary objective is to obtain the shortest spindown time. However, the solutions for all prediction methods should be checked to confirm their equality. Figure 3-1: The Simple Channel Flume Model Table 3-2: Prediction Results for FESWMS Simple Channel Flume No Prediction Linear Predictions Quadratic Predictions Mixed Predictions Wave Effect Predictions Loading Combination Total Time Number of Runs Total Time Number of Runs Total Time Number of Runs Total Time Number of Runs Total Time Number of Runs Geo 0: : : :26 11 Unsuccessful WSE 0: : : : :33 11 Geo and WSE 0: : : :59 19 Unsuccessful Geo and Eddy 0: : : :24 11 Unsuccessful Geo and Flow 1: : : :33 16 Unsuccessful WSE and Eddy WSE and Flow Geo, WSE, and Eddy Geo, WSE, and Flow Geo, Eddy, and Flow WSE, Eddy, and Flow Geo, WSE, Eddy, and Flow 0: : : : :34 11 Unsuccessful Unsuccessful Unsuccessful Unsuccessful Unsuccessful 0: : : :42 14 Unsuccessful Unsuccessful Unsuccessful Unsuccessful Unsuccessful Unsuccessful 1: : : :33 16 Unsuccessful 2: : :11 22 Unsuccessful 0: : : : :37 13 Unsuccessful 39

61 Each prediction method produced identical solution files. Therefore, this research may equally compare the spindown times. Linear, quadratic, and mixed prediction methods reduced the total spindown time and number of runs for most steering combinations involving geometry. Wave effect predictions worked well for spinning on water surface elevation, but produced unsuccessful results for combinations including geometry. The best spindown times (highlighted in bold) came from linear, quadratic, and mixed predictions spinning on geometry or geometry and eddy viscosity. Based on these results, this research recommends linear, quadratic, or mixed predictions for steering combinations that include geometry but do not include water surface elevation. Each of these prediction methods produced nearly equal results for these combinations. This research also recommends wave effect predictions for combinations that include water surface elevation but do not include geometry. Wave effect predictions produced nearly identical results compared to using no predictions except for the steering combination of water surface elevation, eddy viscosity, and flow rate. Another test is needed to confirm these recommendations and to help identify a possible prediction method for combinations including both water surface elevation and geometry. The second test involved the more complicated Capitol Reef model as shown in Figure 3-2. Table 3-3 displays the results for all prediction methods. 40

62 Figure 3-2: The Capitol Reef Model Table 3-3: Prediction Results for Capitol Reef No Prediction Linear Predictions Quadratic Predictions Mixed Predictions Wave Effect Predictions Loading Combination Total Time Number of Runs Total Time Number of Runs Total Time Number of Runs Total Time Number of Runs Total Time Number of Runs Geo 5: : : : :55 18 WSE 4: : : : :13 23 Geo and WSE 5: : : : :29 14 Geo and Eddy 6: : : : :01 18 Geo and Flow 7: : : : :53 18 WSE and Eddy 2: : : : :58 9 WSE and Flow Unsuccessful Unsuccessful Unsuccessful Unsuccessful Unsuccessful Geo, WSE, and Eddy 4: : : : :19 14 Geo, WSE, and Flow 5: : : : :34 14 Geo, Eddy, and Flow 5: : : : :54 18 WSE, Eddy, and Flow Unsuccessful Unsuccessful Unsuccessful Unsuccessful Unsuccessful Geo, WSE, Eddy, and Flow 3: : : : :

63 Again, each prediction method produced nearly identical solution files with only negligible differences. Linear, quadratic, and mixed prediction methods reduced the total spindown time for almost all steering combinations. The wave effect prediction method was also effective for most steering combinations, especially for those that included water surface elevation. Wave effect predictions even outperformed all other prediction methods for two steering combinations that did not use spinning on water surface elevation, including the combination of geometry and flow rate and the combination of geometry, eddy viscosity, and flow rate. However, the other prediction methods performed nearly as well as the wave effect predictions for these two combinations. The best spindown time came from wave effect predictions spinning on water surface elevation and eddy viscosity. These results confirm the previous suggestions in the Simple Channel Flume to use linear, quadratic, and mixed predictions for steering combinations that include geometry but do not include water surface elevation, and to use wave effect predictions for combinations that include water surface elevation. Combinations that include both water surface elevation and geometry need further review. Linear, quadratic, and mixed predictions have problems predicting the sharp break in the trends when steering on water surface elevation. Wave effect predictions handled these combinations effectively in the Capitol Reef model, but not in the Simple Channel Flume. This inconsistency comes from how the wave effect prediction handles the changing geometry and the prediction of negative depths. Since the water level drops as the geometry rises for this combination, it often predicts a water surface elevation below the ground elevation for the next step. It handles 42

64 negative depths by setting the water surface elevation between the final ground elevation and the water surface elevation from the previous step. This worked well for the Capitol Reef model, but not for the Simple Channel Flume. This research also tried handling the problem by setting the water surface elevation to the ground elevation of the next step plus half of the water depth from the previous step. This worked well for the Simple Channel Flume, but not for the Capitol Reef model. Therefore, more research is recommended to best handle the prediction of negative depths. The best prediction methods according to the spin down times for each model and loading combination are summarized in Table 3-4. Methods with spindown times within two seconds of the fastest method s time and with the same number of total steps are included in the table. The percent change compares the best prediction time to the spindown time without using predictions. A negative value represents improvement. Table 3-4: Best Prediction Methods FESWMS Simple Channel Flume Capitol Reef Percent Percent Loading Combination Best Method Change Best Method Change Geo Linear/Quadratic/Mixed -50% Linear -73.2% WSE None/Wave Effect 0.0% Wave Effect -28.5% Geo and WSE None 0.0% Wave Effect -74.1% Geo and Eddy Linear/Quadratic/Mixed -51.0% Quadratic -80.1% Geo and Flow Linear/Quadratic/Mixed -48.4% Wave Effect -73.3% WSE and Eddy None/Wave Effect 0.0% Wave Effect -60.8% WSE and Flow Unsuccessful ---- Unsuccessful ---- Geo, WSE, and Eddy Linear -2.6% Wave Effect -71.4% Geo, WSE, and Flow Unsuccessful ---- Wave Effect -72.0% Geo, Eddy, and Flow Linear/Quadratic/Mixed -49.2% Wave Effect -67.2% WSE, Eddy, and Flow Wave Effect -60.5% Unsuccessful ---- Geo, WSE, Eddy, and Flow Mixed -14.0% Wave Effect -50.4% 43

65 This evidence suggests using linear, quadratic, or mixed predictions for steering combinations that include geometry but not water surface elevation and to use wave effect predictions for combinations that include water surface elevation. Combinations including both geometry and water surface elevation require further research. Wave effect predictions may or may not be used for these combinations depending on the model. Perhaps in the future, the user could have the option to choose the prediction method. Linear predictions were implemented into SMS for steering combinations that include geometry but not water surface elevation. This research also implemented wave effect predictions for all combinations that include water surface elevation. Since the effectiveness of combinations that include both geometry and water surface elevation depends on the model, this research does not recommend these combinations. Wave effect predictions were not implemented for RMA2. Since RMA2 runs a separate FORTRAN executable to create predicted hotstart files, implementing wave effect predictions for RMA2 required extensive FORTRAN coding that was not within the expertise and scope of this research. However, future work in this area is recommended. Linear predictions for all steering combinations were implemented for RMA Results In general, the creation of predictions resulted in substantial improvements in the spindown process. A comparison of the before and after predictions shows a 44

66 considerable decrease in the number of steps and the computation time of the spindown. The total spindown time is measured instead of the number of iterations since the ultimate goal is to minimize the computation time. All the solution files produced in this section were nearly identical with the exception of two steering combinations in the RMA2 Tributary. The combination of geometry and flow rate and the combination of geometry, eddy viscosity, and flow rate for the original results (without predictions) produced slightly higher water surface elevations and velocities. Predictions created solutions consistent with all other solutions for these combinations. Table 3-5 and Figure 3-3 illustrate the changes with predictions for the RMA2 Simple Channel Flume. Figure 3-3 only shows the steering combinations that were successful before and after the changes. Predictions actually slowed down the spindown process, especially for steering combinations that include water surface elevation. Linear predictions are not very effective when spinning on water surface elevation for this model. However, notice that predictions do not increase the total number of runs for some of the combinations. The spindown time is higher because of the time it takes to create the prediction between each step. Most combinations that included flow rate failed because of the instability of low flow through this channel. Low flow causes all of the floodplain elements to dry, but the channel alone has difficulties conveying the flow. These results suggest spinning on geometry or geometry and eddy viscosity in the absence of wave effect predictions. 45

67 Table 3-5: RMA2 Simple Channel Flume Results with Predictions Original With Predictions Percent Change Loading Combination Total Number Total Number Total Number Time of Runs Time of Runs Time of Runs Geo 0:11 4 0: % 0.0% WSE 0: : % 0.0% Geo and WSE 0: : % 25.0% Geo and Eddy 0:11 4 0: % 0.0% Geo and Flow Unsuccessful Unsuccessful WSE and Eddy 0: : % 0.0% WSE and Flow 0:28 16 Unsuccessful Geo, WSE, and Eddy 0: : % 25.0% Geo, WSE, and Flow Unsuccessful Unsuccessful Geo, Eddy, and Flow Unsuccessful Unsuccessful WSE, Eddy, and Flow 0:28 16 Unsuccessful Geo, WSE, Eddy, and Flow Unsuccessful Unsuccessful Prediction Results Spindown Time (min) Geo WSE Geo and WSE Geo and Eddy WSE and Eddy Geo, WSE, and Eddy Steering Combination Original With Predictions Figure 3-3: RMA2 Simple Channel Flume Results with Predictions 46

68 Note that when spinning on geometry in RMA2, the model runs gfgen before each step because of the changing bathymetry. Therefore, combinations that include geometry may run slower. For example, the combination of geometry, water surface elevation, and eddy viscosity and the combination of water surface elevation, eddy viscosity, and flow rate both took 16 steps. However, the combination including geometry took 50 seconds where the other combination only took 28 seconds. Predictions in the FESWMS Simple Channel Flume improved the spindown time for most of the steering combinations as shown in Table 3-6 and Figure 3-4. Some tests before predictions did not have any runs fail after the first two successful runs (for example, steering on water surface elevation). In these cases, predictions could decrease the number of iterations per step, but not the number of steps. Therefore, the spindown times with predictions are nearly the same or longer because of the time to create the predictions. The step following two successful runs could be increased, but this would have a negative effect on models that require a smaller step size throughout the spindown. Consequently, predictions are more effective on more complex models that have runs fail throughout the spindown. As noted earlier, wave effect predictions were not effective for steering combinations that included both geometry and water surface elevation in the FESWMS Simple Channel Flume. This research does not recommend using these steering combinations due to their inconsistency between models. The best spindown times came from spinning on geometry or geometry and eddy viscosity. 47

69 Table 3-6: FESWMS Simple Channel Flume Results with Predictions Original With Predictions Percent Change Loading Combination Total Number Total Number Total Number Time of Runs Time of Runs Time of Runs Geo 0: : % -42.1% WSE 0: : % 0.0% Geo and WSE 0:51 17 Unsuccessful Geo and Eddy 0: : % -42.1% Geo and Flow 1: : % -38.5% WSE and Eddy 0: : % 0.0% WSE and Flow Unsuccessful Unsuccessful Geo, WSE, and Eddy 0:38 13 Unsuccessful Geo, WSE, and Flow Unsuccessful Unsuccessful Geo, Eddy, and Flow 1: : % -23.1% WSE, Eddy, and Flow 2: : % -54.3% Geo, WSE, Eddy, and Flow 0:43 15 Unsuccessful Prediction Results 2.5 Spindown Time (min) Geo WSE Geo and Eddy Geo and Flow WSE and Eddy Geo, Eddy, and Flow WSE, Eddy, and Flow Steering Combination Original With Predictions Figure 3-4: FESWMS Simple Channel Flume Results with Predictions 48

70 The RMA2 Tributary gives results (Table 3-7 and Figure 3-5) somewhat inconsistent with the previous two tests. Predictions for the most part reduced the spindown time, but the best times actually came from steering combinations that included water surface elevation and not geometry. The results with predictions for steering on geometry and the combination of geometry and eddy viscosity were nearly identical to those without predictions. Overall the results show considerable improvements for predictions. It is interesting to note how well linear predictions perform for steering combinations that include water surface elevation in this test. This may occur because the solution has a relatively flat water surface elevation, and linear predictions do not overshoot as far past the sharp break in the water surface elevation and velocity trends. Table 3-7: RMA2 Tributary Results with Predictions Original With Predictions Percent Change Loading Combination Total Number Total Number Total Number Time of Runs Time of Runs Time of Runs Geo 0: : % 0.0% WSE 0: : % -66.7% Geo and WSE Unsuccessful Unsuccessful Geo and Eddy 0: : % 0.0% Geo and Flow 3: : % -44.8% WSE and Eddy 0: : % -66.7% WSE and Flow 0: : % -66.7% Geo, WSE, and Eddy Unsuccessful Unsuccessful Geo, WSE, and Flow 3: : % -46.7% Geo, Eddy, and Flow 3: : % -44.8% WSE, Eddy, and Flow 0: : % -66.7% Geo, WSE, Eddy, and Flow 3: : % -46.7% 49

71 Prediction Results Spindown Time (min) Geo WSE Geo and Eddy Geo and Flow WSE and Eddy WSE and Flow Geo, WSE, and Flow Geo, Eddy, and Flow Steering Combination WSE, Eddy, and Flow Geo, WSE, Eddy, and Flow Original With Predictions Figure 3-5: RMA2 Tributary Results with Predictions The results for the Capitol Reef model (Table 3-8 and Figure 3-6) show the most consistent improvements for predictions. Predictions provided considerable improvements for all steering combinations and did not cause any additional combinations to fail. The model spins down nearly 3 to 4 times faster for all steering combinations except water surface elevation. Combinations including geometry gave some of the best improvements, but the best time came from wave effect predictions for the steering combination of water surface elevation and eddy viscosity. 50

72 Table 3-8: FESWMS Capitol Reef Results with Predictions Original With Predictions Percent Change Loading Combination Total Number Total Number Total Number Time of Runs Time of Runs Time of Runs Geo 5: : % -68.3% WSE 4: : % -23.3% Geo and WSE 5: : % -68.2% Geo and Eddy 6: : % -64.4% Geo and Flow 7: : % -57.7% WSE and Eddy 2: : % -55.0% WSE and Flow Unsuccessful Unsuccessful Geo, WSE, and Eddy 4: : % -62.2% Geo, WSE, and Flow 5: : % -66.7% Geo, Eddy, and Flow 5: : % -51.1% WSE, Eddy, and Flow Unsuccessful Unsuccessful Geo, WSE, Eddy, and Flow 3: : % -45.5% Prediction Results Spindown Time (min) Geo WSE Geo and WSE Geo and Eddy Geo and Flow WSE and Eddy Geo, WSE, and Eddy Geo, WSE, and Flow Steering Com bination Geo, Eddy, and Flow Geo, WSE, Eddy, and Flow Original With Predictions Figure 3-6: FESWMS Capitol Reef Results with Predictions 51

73 52

74 4 The Spindown Step Size The spindown step size defines the algorithm SMS uses to determine each step size during the spindown process. Optimally, the model would take the largest step possible for every run without causing any failures, while minimizing the number of iterations per step. However, due to the variety of conditions, this is impossible. This research uses the basic idea of decreasing the step size after a failed run and slightly increasing the step size after a successful run. It uses different combinations of this idea in an attempt to decrease the spindown computation time for all models using a trial-and-error approach. The original method caused SMS to decrease the step size to one-half the step if the run failed. If the run was successful, then the step would be multiplied by 1.1 after the 2 nd consecutive successful step. The following two sections describe the changes made to the original method of determining the step size and the bugs fixed in the steering module. 4.1 Step Size Changes The new method changes the determination of the next step size after a run. After a successful run, the old method increased the step by 10% only if it was a consecutive successful run. The new method always increases the step size by 10% after a successful run. The decrease after a failed run now depends on how many 53

75 consecutive runs have failed. After the first failure, the step is divided by The second, third, and fourth consecutive failed steps are divided by 1.5, 1.75, and 2.0 respectively. If more than four consecutive failures occur, then the step is always divided by 2.0. Table 4-1 summarizes the new procedure with an example starting at a step size of 15.0%. Table 4-1: Procedure for Decreasing Sizes of Failed Steps Number of Failures Division Factor Next Step Size Old Version Step Size for 1st Attempt N/A 15.00% 15.00% 1st Failure % 7.50% 2nd Failure % 3.75% 3rd Failure % 1.88% 4th Failure % 0.94% 5th Failure % 0.47% The smaller decrements at the beginning of failing runs allow the model to quickly rebound. In fact, if a successful run follows two failed runs, the model will attempt a spin down value higher than the attempted value before the first failure as illustrated with an example in Table 4-2. The same example in Table 4-3 shows the slow rebound of the old spindown method as a comparison. These results also explain that if a successful run follows two failed runs that the next step size for the new method would be over twice the next step size for the old method (2.93% compared to 1.25%). 54

76 Table 4-2: Quick Rebound Example of the New Spindown Method Last Outcome Current Value Step Size Factor Next Step Size Attempted Value Result Success 10.00% N/A 5.00% 15.00% Failure Failure 10.00% % (5.00/1.25) 14.00% Failure Failure 10.00% % (4.00/1.50) 12.67% Success Success 12.67% % (2.67*1.10) 15.60% ---- Table 4-3: Slow Rebound Example of the Old Spindown Method Last Outcome Current Value Step Size Factor Next Step Size Attempted Value Result Success 10.00% N/A 5.00% 15.00% Failure Failure 10.00% % (5.00/2.00) 12.50% Failure Failure 10.00% % (2.50/2.00) 11.25% Success Success 11.25% % (1.25*1.00) 12.50% ---- This research tested another possible method which used a division factor of 1.5 for the first, second, and third consecutive failed runs. It then used a division factor of 2.0 for four or more consecutive failed runs or if the model was within 1% of completing the spindown process. This alternative was not as effective. The final alteration to the step size algorithm included setting up a maximum step size. SMS invokes a maximum step size when a failed run follows four or more consecutive successful runs. It sets the value of the maximum step size equal to the step size used in the last successful run as long as this step size is at least 1% of the total spindown. SMS then uses this maximum step size for the remaining steps of the spindown process. If a failure occurs, then the maximum step size is no longer used. The maximum step size helps prevent the model from taking large steps that have a high probability of failure. Table 4-4 gives an example to illustrate how this works (maximum step size is abbreviated as MSS). 55

77 Table 4-4: Using the Maximum Step Size Last Outcome Current Value Step Size Factor Next Step Size Attempted Value Result Success 10.00% N/A 5.00% 15.00% Success Success 15.00% % (5.00*1.10) 20.50% Success Success 20.50% % (5.50*1.10) 26.55% Success Success 26.55% % (6.05*1.10) 33.21% Failure Failure 26.55% Use MSS 6.05% (from last step) 32.60% Success Success 32.60% Use MSS 6.05% 38.65% Success Success 38.65% Use MSS 6.05% 44.70% Failure Failure 38.65% % (6.05/1.25) 43.49% Success Success 43.49% % (4.84*1.10) 48.81% Success Success 48.81% % (5.32*1.10) 54.67% Minimizing Delays Six problems were identified which added time to the spindown process: 1. FESWMS sometimes ran the maximum number of iterations even when the run had clearly diverged. 2. SMS interpreted runs whose average depth change between iterations oscillating near zero as a failure. 3. SMS would allow the model to take the minimum step twice consecutively before aborting the steering process. 4. Models would not finish spinning down if their last step was within the minimum step. 5. One mode (geometry, water surface elevation, eddy viscosity, or flow rate) could spin down past the 100% mark while another mode had not yet reached 100% spun down. 6. All modes did not reach 100% spun down simultaneously. 56

78 The first problem was resolved by automatically aborting the current run if the maximum water surface elevation change between steering iterations exceeded 100 for FESWMS. This eliminated the needless iterations that would occur after large water surface elevation differences of a failing run. RMA2 already contained a built-in maximum water surface elevation change between steering iterations. In the past the developers of RMA2 had set this maximum depth convergence parameter to 25 ft. (USACE 2005). However, after running numerous tests, it appears that they have recently increased it to 50 ft. The next problem involved how SMS determined if a FESWMS steering run had succeeded. In the past SMS incremented one variable if the average change in water surface elevation became larger between iterations (diverging) and another variable if the average change in water surface elevation became smaller between iterations (converging). The number of converging iterations and diverging iterations were then compared. If the number of converging iterations added up to over 1.5 times the number of diverging iterations and the final maximum change in water surface elevation was less then 0.1, then SMS declared the run successful. However, this became a problem with oscillating runs. If the model oscillates with changes in water surface elevation near zero, then the run would fail. This result proved undesirable because oscillations should be ignored when the changes in water surface elevation are negligible. The model would still give a good answer. The solution to this problem included only incrementing the number of diverging iterations if the average change in water surface elevation between iterations became larger by at least This way if a model oscillates near zero, the number of 57

79 diverging iterations will not increment. Additionally, SMS overrides the convergence algorithm if the final maximum change in water surface elevation is less than This way if the model is extremely stable at the end of a run, it will always succeed. The next problem s fix consisted of allowing the model to take the minimum step only one time consecutively during the steering process. Previously the model would take the minimum step two times consecutively before aborting the steering process. The last three problems involved the conclusion of the steering process. The results of fixing these bugs included performing the final step of a steering process even if it was within the minimum step, not allowing any of the steering modes to spin down past 100%, and making sure that all steering modes reached 100% simultaneously. Fixing the first of the three problems included waiting until all steering modes reached 100% within a given tolerance before terminating the steering process. Eliminating the initial condition and minimum step edit fields on the steering dialog fixed the latter two problems. When the initial conditions and minimum steps automatically set themselves, all steering modes reach 100% together and cannot cross the 100% mark. 4.3 Results The alteration of the step size did not improve the spin down speed nearly as much as the creation of predictions. It helped some situations, but at the same time hurt others. The results of this research demonstrate the difficulty in finding a step size algorithm that positively affects all models and steering combinations. The 58

80 following four tables present the results of the modified steps compared to the original method for the RMA2 and FESWMS Simple Channel Flumes, Tributary, and Capitol Reef. Table 4-5 and Figure 4-1 show the results for the RMA2 Simple Channel Flume. Since all the solution files produced in this section were nearly identical, the spindown times may be compared equally. These results did not include predictions. Table 4-5: RMA2 Simple Channel Flume Results with New Steps Original With New Steps Percent Change Loading Combination Total Number Total Number Total Number Time of Runs Time of Runs Time of Runs Geo 0:11 4 0: % 25.0% WSE 0: : % 9.1% Geo and WSE 0: : % 43.8% Geo and Eddy 0:11 4 0: % 25.0% Geo and Flow Unsuccessful 1: WSE and Eddy 0: : % 9.1% WSE and Flow 0:28 16 Unsuccessful Geo, WSE, and Eddy 0: : % 43.8% Geo, WSE, and Flow Unsuccessful Unsuccessful Geo, Eddy, and Flow Unsuccessful 1: WSE, Eddy, and Flow 0:28 16 Unsuccessful Geo, WSE, Eddy, and Flow Unsuccessful Unsuccessful

81 New Step Size Results Spindown Time (min) Geo WSE Geo and WSE Geo and Eddy Steering Combination WSE and Eddy WSE and Flow Original With New Steps Figure 4-1: RMA2 Simple Channel Flume Results with New Steps The new modified steps helped two steering combinations succeed that had previously failed, but they actually increased the spindown time for all other combinations and caused two other combinations to fail. The modified steps do not help models that spin down in a small number of steps. Since the model tries to take larger steps, it causes more failures. For this reason the total number of steps and total spindown time may increase even if the number of successful runs does not increase. In the cases where the modified steps caused a combination to fail that originally succeeded, or vice versa, these combinations all included steering on flow rate. Research showed that this model was very sensitive to the amount of flow running through the channel. Lower flows caused all the floodplain elements to dry, but at the same time the channel could not contain the entire flow. This caused instability for 60

82 certain flow rates. These results suggest avoiding steering on flow rate when several elements may simultaneously dry when decreasing the flow. The modified steps did not affect which steering combinations spun down the fastest. Table 4-6 and Figure 4-2 present the step size results for the FESWMS Simple Channel Flume. The modified steps had relatively small effects except when steering on geometry and water surface elevation. The modified steps adversely affected this combination. The combination of water surface elevation and eddy viscosity remained the most efficient, but the modified steps slowed down spinning on water surface elevation from 33 seconds to 44 seconds. Generally, the modified steps performed better on the steering combinations that required more runs. Table 4-6: FESWMS Simple Channel Flume Results with New Steps Original With New Steps Percent Change Loading Combination Total Number Total Number Total Number Time of Runs Time of Runs Time of Runs Geo 0: : % 10.5% WSE 0: : % 36.4% Geo and WSE 0: : % 94.1% Geo and Eddy 0: : % 10.5% Geo and Flow 1: : % -7.7% WSE and Eddy 0: : % 0.0% WSE and Flow Unsuccessful Unsuccessful Geo, WSE, and Eddy 0: : % 38.5% Geo, WSE, and Flow Unsuccessful Unsuccessful Geo, Eddy, and Flow 1: : % -11.5% WSE, Eddy, and Flow 2: : % -17.1% Geo, WSE, Eddy, and Flow 0: : % 13.3% 61

83 New Step Size Results Spindown Time (min) Geo WSE Geo and WSE Geo and Eddy Geo and Flow WSE and Eddy Geo, WSE, and Eddy Geo, Eddy, and Flow WSE, Eddy, and Flow Steering Combination Geo, WSE, Eddy, and Flow Original With New Steps Figure 4-2: FESWMS Simple Channel Flume Results with New Steps Table 4-7 and Figure 4-3 present the results for the RMA2 Tributary model. The modified steps had a much more dramatic effect to the results in the RMA2 Tributary than it did for the previous two examples. Other than the loading of geometry, the combination of geometry and eddy viscosity, and the combination of geometry, WSE, and flow rate, the modified steps had completely favorable results. In fact, many of the loading combinations saw a 50% or more reduction in the spindown time and total number of steps. The modified steps did not affect which steering combinations spun down the fastest. 62

84 Table 4-7: RMA2 Tributary Results with New Steps Original With New Steps Percent Change Loading Combination Total Number Total Number Total Number Time of Runs Time of Runs Time of Runs Geo 0: : % 45.5% WSE 0: : % -50.0% Geo and WSE Unsuccessful Unsuccessful Geo and Eddy 0: : % 45.5% Geo and Flow 3: : % -34.5% WSE and Eddy 0: : % -50.0% WSE and Flow 0: : % -50.0% Geo, WSE, and Eddy Unsuccessful Unsuccessful Geo, WSE, and Flow 3: : % 46.7% Geo, Eddy, and Flow 3: : % -34.5% WSE, Eddy, and Flow 0: : % -50.0% Geo, WSE, Eddy, and Flow 3: : % 0.0% New Step Size Results Spindown Time (min) Geo WSE Geo and Eddy Geo and Flow WSE and Eddy WSE and Flow Geo, WSE, and Flow Geo, Eddy, and Flow Steering Com bination WSE, Eddy, and Flow Geo, WSE, Eddy, and Flow Original With New Steps Figure 4-3: RMA2 Tributary Results with New Steps 63

85 Table 4-8 and Figure 4-4 present the results for the FESWMS Capitol Reef model. The results for the Capitol Reef model range from a spindown time reduction of 25.7% for the loading combination of geometry, WSE, and eddy viscosity to an increased spindown time of 49.1% when all steering parameters are loaded. The modified steps produced favorable time reductions for nearly half of the loading combinations, but failed in all the others. Once again, the modified steps did not affect which steering combination spun down the fastest. It is difficult to determine if the modified steps had an overall positive effect for the Capitol Reef model. Table 4-8: FESWMS Capitol Reef Results with New Steps Original With New Steps Percent Change Loading Combination Total Number Total Number Total Number Time of Runs Time of Runs Time of Runs Geo 5: : % 2.4% WSE 4: : % 6.7% Geo and WSE 5: : % -6.8% Geo and Eddy 6: : % 8.9% Geo and Flow 7: : % 15.4% WSE and Eddy 2: : % 10.0% WSE and Flow Unsuccessful Unsuccessful Geo, WSE, and Eddy 4: : % -24.3% Geo, WSE, and Flow 5: : % -2.4% Geo, Eddy, and Flow 5: : % 28.9% WSE, Eddy, and Flow Unsuccessful Unsuccessful Geo, WSE, Eddy, and Flow 3: : % 33.3% 64

86 New Step Size Results Spindown Time (min) Geo WSE Geo and WSE Geo and Eddy Geo and Flow WSE and Eddy Geo, WSE, and Eddy Geo, WSE, and Flow Steering Com bination Geo, Eddy, and Flow Geo, WSE, Eddy, and Flow Original With New Steps Figure 4-4: FESWMS Capitol Reef Results with New Steps 65

87 66

88 5 Recommendations to Best Utilize the Steering Module Users must specify which steering combinations to employ as well as initial condition and minimum step percentages to run the steering module. This chapter gives recommendations to help the user enter these inputs to best utilize the steering module. 5.1 Initial Condition and Minimum Value Percentages Many users have expressed confusion in how to use the steering module dialog. If the user wanted to spin on water surface elevation, the dialog required an initial condition percentage and a minimum step percentage. To specify the initial condition percentage, the user had to know what initial water surface elevation to use, divide this value by the actual water surface elevation boundary condition, and multiply by 100 to get a percentage. It was also unclear what percentage to use for the minimum step. Some users were unsure if this meant an actual water surface elevation value or a percentage of the total spindown, and why a minimum percentage was even important. The dialog required these percentages for each steering parameter the user specified (water surface elevation, geometry, eddy viscosity, and flow rate). As a result, this research included simplifying the steering dialog. Instead of entering the initial condition and the minimum step for each type of steering, the modeler may now 67

89 just check the box next to which type(s) of spinning to employ without further user interaction. The initial condition and minimum step variables receive recommended default values within the SMS code. However, the user still has the option of overriding the default initial values if desired. Figure 5-1: Old Steering Dialog Figure 5-2: New Steering Dialog 68