Adaptive Mesh Refinement for Dynamic Rupture Simulations

Jeremy E. Kozdon, & Eric M. Dunham

In Preparation December 2010, SCEC Contribution #6047

The velocity and stress fields near the leading edge of a propagating rupture front are known to be nearly singular [Freund, 1998]. Within a small process zone around the rupture front, r < R0, dynamic friction laws and nonlinear material response prevent a singularity from developing. Laboratory measurements and studies of earthquake nucleation [Rice, 2006; Noda et al., 2009] suggest that R0 ˜ 10 mm, at least in the early stages of rupture, though this is frequently artificially enhanced by several orders of magnitude, R0 ˜ 100 m or even larger, for large-scale earthquake modeling. It is possible that this compromise alters the rupture behavior, though this critical issue remains unexplored because the use of laboratory parameters necessitates millimeter-scale grid spacings around the rupture front. With this requirement, it is computationally infeasible to simulate large-scale ruptures with any method based on a uniform mesh. Problems in which resolution needs are dictated by a small, but dynamically changing, region of the domain are ideally suited for adaptive mesh refinement (AMR) techniques. In this work, we explore the use of the Berger-Oliger AMR framework [Berger and Oliger, 1984; Berger and Colella, 1989] for dynamic rupture simulation. Within this framework, fine scale meshes are added (and removed) dynamically based on the local physics of the problem. Since the meshes are block-structured and overlapping, efficient time integration is possible using local time stepping, that is, each mesh is advanced with a locally optimal time step as opposed to the smallest global time step. Thus the rupture front and sharp wavefronts are resolved using small grid cells and time steps whereas larger grid cells and time steps suffice in areas where the solution is smooth. Preliminary results suggest that the number of grid cells needed by an AMR method for dynamic rupture modeling is several orders of magnitude lower than for a uniform grid, resulting in massive computational and storage savings that far outweigh the additional overhead associated with the more complicated AMR data structures. These results demonstrate the feasibility of AMR for dynamic rupture simulation and, with the inclusion of more complex physics, should enable the use of more realistic friction parameters in large-scale rupture simulations.

Kozdon, J. E., & Dunham, E. M. (2010). Adaptive Mesh Refinement for Dynamic Rupture Simulations. Geophysical Research Letters, (in preparation).

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