1. Exercise Modeling of Hydrosystems: Introduction 1

Transcription

1 1. Exercise Modeling of Hydrosystems: Introduction 1 Informations and tools needed for numerically modeling a hydrosystem: Conceptual model: Geometry of the domain, lengths and hights of the domain Soil properties, geological data (faults, rivers etc.) Boundary conditions Initial conditions for transient problems Spatial dimensions (simplification to 2d or 1d if possible) Equations to describe the problem Method to solve it (FD, IFD, FE,...) Discretization in space and time Program to discretize the equations and solve the algebraic equations Tools for the analysis / visualization...

2 1. Exercise Modeling of Hydrosystems: Introduction 2 In this exercise we will consider a simple example of a hydrosystem: Stady state groundwater flow equation r r r r u = f = ( ) K h q Model GRUWA: 2d Finite Element model with triangular elements Regular rectangular grid -> The model itself is fix, these questions are at the moment not important Purpose of the exercise: Get experience with discretization and boundary conditions

3 1. Exercise Modeling of Hydrosystems: Introduction 3 Requirements for the exercise: Model GRUWA: Numerical simulation of the stady state groundwater flow equation Model Tecplot: Visualization of the flow velocities Please note: With this program we can only model rectangular fields Lenses have to have rectangular shape The corners of lenses have to lie on gridpoints Sinks and sources have to lie on gridpoints

4 Login 1. Exercise Modeling of Hydrosystems: Start 1 user: egw#computer. (#computer is written on the right side of the screen box). E.g. computer 3: egw03 Password: mml#computer. E.g. computer 3: mml03 Login with kde Get started -Click on the icon with the shell at the bottom of the screen -the window with the blue top is the active window. Click on the top part in order to activate the window -change directory in the shell to Wednesday: type cd Wednesday (note: capital letters!!). Wednesday is your working directory. -open tecplot by typing: tecplot &. Note the &!

5 1. Exercise Modeling of Hydrosystems: Start 2 -open Konqueror in order to run GRUWA: click on the button with the house on the bottom of the screen -in the web-address window type: -you can get a large window by clicking on the large square button on the right of the blue top of a window -you can get the window off the screen by clicking on the small square button at the blue top of the window. You can resize the window by clicking at the application in the middle field at the bottom of the screen. Input form of GRUWA -Grid discretization -Material properties -Lenses -Boundary conditions -Sources and sinks -Output

6 1. Exercise Modeling of Hydrosystems: GRUWA 1 Grid discretization: 4 Note: M*N has to be <= 9500

7 1. Exercise Modeling of Hydrosystems: GRUWA 2 -Material properties and lenses: Click to activate!!! Set always 0

8 1. Exercise Modeling of Hydrosystems: GRUWA 3 -Examples for lenses:

9 1. Exercise Modeling of Hydrosystems: GRUWA 4 -Boundary conditions: NW North NE West East SW South SE Dirichlet: [m], Neumann: [m^3/s]. Note: Neumann is given at the nodes. The unit is not as usual [m/s]. Therefore, increasing the number of cells without decreasing the value of the Neumann condition at the cells yields higher outflow!! This is specific for GRUWA

10 1. Exercise Modeling of Hydrosystems: GRUWA 5 -Sources and sinks: Click to activate!!! -Output: Click to submit

11 1. Exercise Modeling of Hydrosystems: GRUWA 6 -Output of the simulation: 2d-graphics of the piezometric heads Output files: We only need the tecplot-output for visualization of velovities. If you need to look at the velocities: Click with the right mouse on filename.plt and keep the botton pressed. Choose from the menu: Save link as.... Remember to save the files in the directory Wednesday

12 1. Exercise Modeling of Hydrosystems: Tecplot Activate the tecplot window. Visualization of the velocities with tecplot: Read in the data file. In the Menu File go to Load DataFile(s) and click on the file you want to look at. Note: Files should be in the directory Wednesday!! Load the Style. Go to the Menu Style and click on Paste Style From File. Select 'GRUWA.sty from the 'Wednesday' directory. Visualize the vectors: Click on 'Vector' in the menu on the left side. Select the components: U-> V4: VX and V-> V5: VY Change the length of the vectors if necessary: In the Menu Field select Vektor Length and change the number by e.g. an order of magnitude. Change Contour-Levels if necessary: In the menu Field select Contour Levels and click e.g. on 'Reset Levels If you want to read in a new file, close the old one by choosing in File the New Layout field. Do not save the layout when closing it.

13 1. Exercise Modeling of Hydrosystems: Ex. 1and m 1000 m impermeable These exercises do not require tecplot! y h = 100 m K f = m/s h = 90 m Figure 1 impermeable x Ex. 1: Calculate the heads for the whole area shown above using GRUWA. Use elements of x= y=20 m. Be careful with the boundary conditions. What are the right boundary conditions at the corners? Ex. 2: Do the same exercise as Exercise 1, but insert a producing well in the middle of the domain. This well should produce with a rate of m 3 /s. Try coarse and fine discretizations. How does the resulting head change with the discretization? What is more realistic?

14 1. Exercise Modeling of Hydrosystems: Ex m 1000 m impermeable K f 1 = m/s y h = 100 m K f 1 K f 2 h = 80 m Figure 2 Ex. 3: x impermeable Include a lense of 100 x 100 meters. The corners of the lense has to coincide with grid nodes. The boundary conditions are as shown in Figure 2. Set the permeability of the lense to 10 times, 0.1 times and 0.01 times of K f1. Visualize the flow velocities with tecplot. How does the lense change the velocity field?

15 1. Exercise Modeling of Hydrosystems: Ex. 4 K f 1 = m/s K f 2 = m/s Use the same model as in Ex. 1. Discretize in 80 x 20 cells. Include lenses to generate the three permeability constellations shown above (you need two lenses for the first two and eight for the last one). Visualize here in tecplot only the x-component of the flow velocity. The easiest way to do this is to load the data file, but to load not the style file GRUWA.sty. Instead switch off the mesh by clicking on the mesh button on the left hand side. Then click on contour and select V4: VX. You can also go to Field on the menu on the top, select Contour variable and select V4: VX. Then go to Field, Contour Attributes and choose under Contour Plottype the option Flood. Then go to Field, Contour Legend and click on Show Contour Legend.

16 1. Exercise Modeling of Hydrosystems: Ex. 4 Try to get an estimate (the exact number is not important), how big the average velocity in x-direction over the domain is. Compare the estimated averaged velocities for the three cases. How could you interpret the result? If you do not have enough time, just compare the first two cases.

17 1. Exercise Modeling of Hydrosystems: End Please close all your programs Please logout of the shell with exit Please click on the exit button on the bottom of the screen (that is the button underneath the button with the lock) and switch off the screen Please put back the keybord and the mouse. GIMOLUS will be introduced by Dr. Maren Paul. For access to: (Send your first name, surname, address and matrikel number, and inicate if your data may be logged).