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Adaptive Mesh Refinement for Dynamic Rupture Simulations

Tetemoko Adaptive Mesh Refinement for Dynamic Rupture Simulations by Jeremy E. Kozdon and Eric M. Dunham from Stanford University utilizes high-resolution requirements localized in space and time for earthquake simulations. It introduces Block-Structured AMR using Chombo, a C++ code developed at Lawrence Berkeley National Lab, capable of handling linear elasticity and boundary data for seismic events.

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Adaptive Mesh Refinement for Dynamic Rupture Simulations

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  1. TetemokoAdaptive Mesh Refinement for Dynamic Rupture Simulations Jeremy E. Kozdon Eric M. Dunham Department of Geophysics, Stanford University

  2. Motivation Fields close to edge of propagating rupture are nearly ~ r-1/2 for r > R0 Experiments and theory suggest R0 ~ 10mm requiring grid resolutions < 1mm Slip pulse time history for a 32m meter rupture with 0.5mm grid spacing (From Noda et al. (2009)) 100km fault requires 108 grid points (~1016 in full domain) Not possible with current simulation technology SCEC :: Kozdon & Dunham :: Tetemokoement

  3. Motivation But… high resolution requirements are localized in space and time! Solution derived from Rice(2005) SCEC :: Kozdon & Dunham :: Tetemokoement

  4. Chombo: Block-structured AMR Chombo Swahili for “box”, “container”, or “useful thing” Developed at Lawrence Berkeley National Lab C++ (AMR data structures) with FORTRAN solvers Compartmentalized code (out-of-the-box solvers) but easy to add our own Both 2-D and 3-D with a single code Seen to scale well on thousands of cores Actively developed Default solver is a unsplit, upwind, multi-D, 2nd order finite volume method (but can add/develop own “easily”) SCEC :: Kozdon & Dunham :: Tetemokoement

  5. Tetemoko: Earthquakes with Chombo Tetemoko: Swahili for “earthquake” Extension of Chombo to handle the linear elasticity with boundary/interface data (i.e., friction variables) Current version: V.1.0 – single interface with symmetry and homogeneous domain SCEC :: Kozdon & Dunham :: Tetemokoement

  6. Adaptive Mesh Refinement (AMR) problem: different portions of domain require different levels of resolution for same accuracy idea: adapt method/grid to local resolution needs Block-structured refinement: SCEC :: Kozdon & Dunham :: Tetemokoement

  7. Block-Structured AMR Each level advanced with locally optimal time step synchronize levels 1 & 2 synchronize levels 0 & 1 tn+1 Time synchronize levels 1 & 2 tn Level 2 Level 0 Level 1 SCEC :: Kozdon & Dunham :: Tetemokoement

  8. Finite Difference Finite Volume Work with point values Work with cell averages Equation in differential form Equation in integral form Approximation of derivatives Approximation of integral fluxes must be reconstructed from cell averages SCEC :: Kozdon & Dunham :: Tetemokoement

  9. Upwind Finite Volume Methods Consider anti-plane problem Split into right and left going waves Define “face” state using waves propagating into face Flux defined from assume constant face state over time SCEC :: Kozdon & Dunham :: Tetemokoement

  10. Unsplit, 2nd order Finite Volume Method Split methods use dimensional fluxes: SCEC :: Kozdon & Dunham :: Tetemokoement

  11. Unsplit, 2nd order Finite Volume Method Unsplit methods use account for transverse waves. First do ½ step with dimensional fluxes SCEC :: Kozdon & Dunham :: Tetemokoement

  12. Unsplit, 2nd order Finite Volume Method Unsplit methods use account for transverse waves. First do ½ step with dimensional fluxes Compute flux using new states SCEC :: Kozdon & Dunham :: Tetemokoement

  13. Enforcing interface conditions Interface conditions are enforced characteristically Split into right and left going waves Define values that satisfy friction law and preserve outgoing wave wave entering domain is then defined from these values Values result from solving radiation damping equation which implies “face” value & flux SCEC :: Kozdon & Dunham :: Tetemokoement

  14. TPV 205-2D 102.4km x 56.2km domain with 100m base resolution 2 levels of refinement (effective resolution: 6.25m) 32 minutes on 64 cores Fault Normal Velocity (m/s) asperity asperity SCEC :: Kozdon & Dunham :: Tetemokoement nucleation

  15. Fault Normal Velocity (m/s) asperity asperity nucleation SCEC :: Kozdon & Dunham :: Tetemokoement

  16. Fx-4.5 SCEC :: Kozdon & Dunham :: Tetemokoement

  17. SCEC :: Kozdon & Dunham :: Tetemokoement

  18. SCEC :: Kozdon & Dunham :: Tetemokoement

  19. SCEC :: Kozdon & Dunham :: Tetemokoement

  20. Fx-4.5 Finest Mesh Level SCEC :: Kozdon & Dunham :: Tetemokoement

  21. AMR Runtime Slope 3 Slope 1.67 SCEC :: Kozdon & Dunham :: Tetemokoement

  22. 3D problem: Slip Velocity Two mesh levels: 100m & 25m SCEC :: Kozdon & Dunham :: Tetemokoement

  23. Tetemoko: Earthquakes with Chombo Tetemoko: Swahili for “earthquake” Extension of Chombo to handle the linear elasticity with boundary/interface data (i.e., friction variables) Current version: V.1.0 – single interface with symmetry and homogeneous domain Planned Development: V.1.1—single interface without symmetry, but symmetric refinement, capable of handling bimaterial problem V.1.2—add capability of handling plasticity (V.1.3—add coordinate transforms?) V.2.0—true multisided interfaces with multiblock grids and coordinate transforms SCEC :: Kozdon & Dunham :: Tetemokoement

  24. FX-7.5 SCEC :: Kozdon & Dunham :: Tetemokoement

  25. FX-12.0 SCEC :: Kozdon & Dunham :: Tetemokoement

  26. FX 0.0 SCEC :: Kozdon & Dunham :: Tetemokoement

  27. FX+4.5 SCEC :: Kozdon & Dunham :: Tetemokoement

  28. FX+7.5 SCEC :: Kozdon & Dunham :: Tetemokoement

  29. FX+12.0 SCEC :: Kozdon & Dunham :: Tetemokoement

  30. Bd-12.0 SCEC :: Kozdon & Dunham :: Tetemokoement

  31. FX+12.0 SCEC :: Kozdon & Dunham :: Tetemokoement

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