Ocean Modeling. Infrastructure (COMI) at LSU

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1 Development of Coastal Ocean Modeling Infrastructure (COMI) at LSU Q. Jim Chen Department of Civil and Environmental Engineering & Center for Computation and Technology Louisiana State University

2 Acknowledgements COMI Team: Drs. Gabrielle Allen, Mayank Tyagi (CCT) Drs. Claes Eskilsson, Kelin Hu (CEE/CCT) Yaakoub El-Khamra, Lei Jiang (CS) Qi Fan, Ranjit Jadhav, Qian Zhang, Haihong Zhao (CEE) Funding: NSF, ONR, NOAA Gulf Shores, Alabama

3 Outline Motivation Combined waves and surge Depth-integrated coastal models Higher-order finite element methods Modeling framework and results Conclusion and future work

4 Louisiana Coastal Protection Assessment of Multiple-lines of Defense Courtesy of Lake Pontchartrain Basin Foundation Animation of Wave-Structure-Seabed Interaction Chen et al. (26)

5 Combined Waves & Surge Bridge damaged by storm waves US -9 bridge over Biloxi Bay, MS Wave overtopping news.bbc.co.uk/.../uk_enl_ /img/1.jpg UK Impact of Katrina on Wetlands Kevork Djansezian/ AP Gulfport, Mississippi during Gustav

6 Challenges Hurricane protection and coastal restoration require a suite of numerical models for different physical processes. Different models use different numerical methods to solve different governing equations, e.g. FDM, FEM, FVM, SEM There is a need for developing a common modeling framework to enable the modeling of multi-physics, multi-scale coastal processes using HPC.

7 Objectives To integrate applicationoriented coastal modeling systems with massiveprocessor, high-performance computing facilities and technologies available at LSU CFD Toolkit Composing Fluid-flow solver To develop the capability of modeling coastal circulation and nearshore surface waves in deltaic environments using highorder numerical methods Solvers Numerics Infrastructure Physics SuperLU Finite difference Cartesian Navier-Stokes Trilinos Finite Volume M-B curvilinear RANS PETSc Spectral Element Unstructured Boussinesq Other coastal models

8 Depth-Integrated Coastal Models Wave Growth Storm Surge Boussinesq-type Equations Wind Stress Mild Slope Equations 3-Dimensional Euler Equations Nonlinear Shallow Water Equations Linear Long Wave Equations Storm Surge

9 Modeling Surge/Wave Attenuation by Porous Media or Vegetation Porous Media Cruz and Chen (27)

10 Why higher-order numerical methods?

11 nstructured Spectral/hp G Methods Solution approximated inside an element by a pth order polynomial expansion (note: can be non-uniform). Supports unstructured meshes (conforming or non-conforming) consisting of elements of size h. Note that the solution is allowed to be discontinuous over the element boundaries. Elements coupled through so-called numerical fluxes (computed by approximate Riemann solvers)

12 CACTUS Framework Successful Applications: Astrophysics, Petroleum Engineering, CACTUS is a freely available, modular, portable and manageable environment for collaboratively developing parallel, highperformance multi-dimensional simulations

13 COMI Architecture UMDriver provides the underlying parallel layer. At present it uses the Zoltan library to provide mesh partitioning, load balancing and mesh migration LocalToGlobal provides local re-indexing of elements, edges and vertices The Nektar++ thorn initializes and populates the data structures of the Nektar++ library MeshReader provides a simple ASCII mesh file reader, and also allows users to (++ Nektar register their own mesh readers (e.g. the mesh reader from The core thorn for the coastal modeling toolkit in Cactus is CoastalWave. This thorn defines the generic variables, parameters, and methods for coastal models Thorn SWE contains the actual SWE solver

14 Nektar++ library Nektar++ is an open-source spectral/hp element library presently in the last stages of ( ) development As the name suggests Nektar++ is written in C++ Nektar++ is developed and maintained by Prof. Sherwin (Imperial College London) and Prof. ( Utah Kirby (University of COMI's shallow water codes are based upon Nektar++ and will be distributed as part of the Nektar++ solver library

15 Discontinuous Galerkin Spectral Element Model Breach Flood Wall Flood wal

16 COMI Result Eskilsson et al. (ICCS 29) Sixth order triangular elements Domain distributed over 8 cores

17 Parallel DG Model

18 Weak Scaling 9 quadrilateral elements per core 1 time steps Times without I/O, initializing and partitioning of the mesh 128 cores, p = 8 roughly 28 million DoF

19 Hurricane Gustav Animation of the combined H*wind and background winds (NCEP/NCAR Reanalysis)

20 Wind Comparison Latitude (degrees) Tide Gages Buoy Stations State Docks C-MAN Stations Meteorology Stations Pensacola Airport Mobile Airport Dauphin Island Sea Lab Station Fort Walton Dauphin Island Perdido Pass Panama Beach Buoy Apalachicola 427 CSBF1 Grand Isle Buoy PSTL1 SW Pass 424 SWP BURL1 Buoy 4239 Wind speed (m/s) Wind speed (m/s) Wind speed (m/s) Wind speed (m/s) Buoy 424 Buoy 427 Dauphin Island PSTL1 SW Pass Aug Sep.1 12 Sep.2 Time (days, Aug.3 ~ Sep.2, 28) Wind direction (degrees) Wind direction (degrees) Wind direction (degrees) Wind direction (degrees) Longitude (degrees) Buoy 424 Buoy 427 Dauphin Island PSTL1 SW Pass Aug Sep.1 12 Sep.2 Time (days, Aug.3 ~ Sep.2, 28)

21 Nested Domain for Wave-Surge Coupling Total triangle elements: 63,757 Total nodes: 32,544. Time step: 4 s Lake Pontchartrain New Orleans ADCIRC Mesh The basin-scale scale mesh provides the open boundary conditions. Both ADCIRC and SWAN are coupled using the same regional mesh. Fine spatial resolution is needed to resolve topographic and hydrodynamic features of flooding and coastal waves.

22 Animation of Modeled Significant Wave Heights (m) during Gustav

23 Modeled Maximum Significant Wave Heights (m) during Gustav

24 Wave Comparison Latitude (degrees) Tide Gages Buoy Stations C-MAN Stations Meteorology Stations Dauphin Island Sea Lab Station State Docks Pensacola Airport Mobile Airport Fort Walton Dauphin Island Perdido Pass Panama Beach Buoy Apalachicola CSBF1 29. Grand Isle PSTL1 SW Pass SWP BURL1 Buoy Buoy Longitude (degrees) Hs (m) Buoy 424 (Red for the observed;blue for the unstructured modeled; Black for the rectangular modeled; Green for the unstructured modeled with no elevation change) 12 W ave period (s) Buoy Hs (m) W ave period (s) Hours from h Hours from h

25 Contribution of Storm Surge to Maximum Significant Wave Heights during Gustav

26 Conclusion and Future Work A coastal modeling framework has been developed at LSU using spectral/hp DG methods and HPC technologies. Effects of vegetation and fluid mud are being incorporated into the solvers. Recent hurricanes provide an excellent testbed for skill assessment of coupled, unstructured surge, wave, salinity and sediment transport models

27 Surge Comparison Latitude (degrees) Tide Gages Buoy Stations C-MAN Stations Meteorology Stations Dauphin Island Sea Lab Station State Docks Pensacola Airport Mobile Airport Fort Walton Dauphin Island Perdido Pass Panama Beach Buoy 427 Apalachicola CSBF1 Grand Isle Buoy PSTL1 SW Pass SWP BURL1 Buoy Longitude (degrees) 2 PSTL1 (red for the observed; blue for the calculated) 2 Dauphin Island (red for the observed; blue for the calculated) Surge (m) 1.5 Surge (m) Panama City 2 Pensacola Surge (m) 1.5 Surge (m) Mobile State Docks Hours from : GDIL Surge (m) 1.5 Surge (m) Hours from : Hours from :

28 Modeled Maximum Surge Heights (m, MSL) during Gustav

29 What is the cause of Katrina s record high surge? Average depth below MSL (m) Chen et al. (28) Katrina Ivan Frederic Distance from shoreline along the track of hurricane (km) Surge Height (m,msl) Sloping Bottom Flat Bottom Distance from shoreline (km)

30 Structure of Cactus Plug-In Thorns ( modules ) driver input/output extensible APIs ANSI C parameters scheduling Core Flesh remote steering Fortran/C/C++ equations of state black holes Reservoir simulators interpolation error handling make system Coastal modelling Molecular dynamics SOR solver grid variables boundary conditions wave evolvers multigrid coordinates

31 A Fully Nonlinear Boussinesq Model for Waves and Currents Continuity Equation η + M = t O 4 ( μ gh ) η = free surface elevation M = volume rate of flow Boussinesq dispersive terms Momentum Equation Momentum mixing term u t α R i + ( u + R α f ) u R w α 2 + g η + μ ( V 4 = O( μ gh l ) Wind forcing 1 + V 2 + V 3 ) Conservation of potential vorticity Wei et al. (1995) and Chen et al. (23, 24, 26)

32 Sea-Dependent Wind Drag Coefficients A new formulation 3 Wind Stress = Skin Friction + Form Drag C 3 d = ( a1 + a2 η x ) + 1 bu Ka=2 a1=.2 a2 = 18 b =.65 Wu (198) C d + Surface slope 3 1 =.8.65U 1 (Sea-independent) C d x ka Large and Pond (81) 1.1 Smith (8) Smith and Banke (75).5 Geernaert et al.(87) Geernaert et al.(86) Sheppard et al. (72).5 Donelan (82) Denman and Miyake (73) Pond et al. (71) Graf et al. (84) U 1 (m/s) (Chen et al, 24)