Tetemoko Adaptive Mesh Refinement for Dynamic Rupture Simulations

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

Motivation Fields close to edge of propagating rupture are nearly ~ r-1/2 for r > R 0 Experiments and theory suggest R 0 ~ 10 mm requiring grid resolutions < 1 mm Slip pulse time history for a 32 m meter rupture with 0. 5 mm grid spacing (From Noda et al. (2009)) 100 km fault requires 108 grid points (~1016 in full domain) Not possible with current simulation technology 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 2

Motivation But… high resolution requirements are localized in space and time! Solution derived from Rice(2005) 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 3

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, 2 nd order finite volume method (but can add/develop own “easily”) 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 4

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 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 5

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: 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 6

Block-Structured AMR tn+1 synchronize levels 0 & 1 levels 1 & 2 Time Each level advanced with locally optimal time step synchronize tn 25 February 2011 levels 1 & 2 Level 0 SCEC : : Kozdon & Dunham : : Tetemokoement Level 1 Level 2 7

Finite Difference Work with point values Finite Volume 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 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 8

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 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 9

Unsplit, 2 nd order Finite Volume Method Split methods use dimensional fluxes: 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 10

Unsplit, 2 nd order Finite Volume Method Unsplit methods use account for transverse waves. First do ½ step with dimensional fluxes 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 11

Unsplit, 2 nd order Finite Volume Method Unsplit methods use account for transverse waves. First do ½ step with dimensional fluxes Compute flux using new states 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 12

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 Values result from solving radiation damping equation 25 February 2011 wave entering domain is then defined from these values which implies “face” value & flux SCEC : : Kozdon & Dunham : : Tetemokoement 13

TPV 205 -2 D 102. 4 km x 56. 2 km domain with 100 m base resolution 2 levels of refinement (effective resolution: 6. 25 m) 32 minutes on 64 cores Fault Normal Velocity (m/s) 25 February 2011 asperity SCEC : : Kozdon & Dunham : : Tetemokoement nucleation asperity 14

Fault Normal Velocity (m/s) asperity 25 February 2011 nucleation SCEC : : Kozdon & Dunham : : Tetemokoement asperity 15

Fx-4. 5 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 16

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Fx-4. 5 Finest Mesh Level 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 20

AMR Runtime Slope 3 Slope 1. 67 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 21

3 D problem: Slip Velocity Two mesh levels: 100 m & 25 m 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 22

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 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 23

FX-7. 5 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 24

FX-12. 0 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 25

FX 0. 0 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 26

FX+4. 5 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 27

FX+7. 5 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 28

FX+12. 0 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 29

Bd-12. 0 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 30

FX+12. 0 25 February 2011 SCEC : : Kozdon & Dunham : : Tetemokoement 31