Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

Abstract

Abstract.A numerical method suitable for wave propagation problems in complex geometries is developed for simulating dynamic earthquake ruptures with realistic friction laws. The numerical method couples an unstructured, node-centered finite volume method to a structured, high order finite difference method. In this work we our focus attention on 2-D antiplane shear problems. The finite volume method is used on unstructured triangular meshes to resolve earthquake ruptures propagating along a nonplanar fault. Outside the small region containing the geometrically complex fault, a high order finite difference method, having superior numerical accuracy, is used on a structured grid. The finite difference method is coupled weakly to the finite volume method along interfaces of collocated grid points. Both methods are on summation-by-parts form. The simultaneous approximation term method is used to weakly enforce the interface conditions. At fault interfaces, fault strength is expressed as a nonlinear function of sliding velocity (the jump in particle velocity across the fault) and a state variable capturing the history dependence of frictional resistance. Energy estimates are used to prove that both types of interface conditions are imposed in a stable manner. Stability and accuracy of the numerical implementation are verified through numerical experiments, and efficiency of the hybrid approach is confirmed through grid coarsening tests. Finally, the method is used to study earthquake rupture propagation along the margins of a volcanic plug. AMS subject classifications: 35L05,35L65,35Q35,65M06,65M08,65M12,65Z05

Summation-by-Parts Operators for Non-Simply Connected Domains

“…are the same type of SBP operators as in (9) but smaller in size (M b and M a , respectively). The notation 0 denotes a zero matrix and the superscript denotes its size (this notation is used throughout the rest of the paper).…”

“…These schemes have so far been mostly developed for spatial domains consisting of simply connected regions. To handle more complicated geometries, hybrid formulations utilizing finite volume and finite difference methods [6,7,8,9] have been proposed. Other alternatives within the finite difference community for complex geometries include finite difference schemes using over-set mesh discretizations [10,11,12,13], multiblock techniques [14,15,16,17], as well as SBP extensions to unstructured grids [18,19,20].…”

Multiblock SBP-SAT Methodology of Symmetric Matrix Form of Elastic Wave Equations on Curvilinear Grids

“…Due to the difficulties associated with the transformation between time and frequency domains, energy estimation was not applicable to the PML within the time domain [48]. A local high-order ABC, as well as a nonreflecting boundary condition (BC), has been widely used for their feasibility, intuitive nature, and generalizability when combined with the SAT method, enabling wellproven approximates [49][50][51][52][53][54][55][56][57][58]. We employed the nonreflecting BC since it provided a simple formulation of the elastic wave problem.…”

A Stable, High Order Accurate and Efficient Hybrid Method for Flow Calculations in Complex Geometries

“…Earlier investigations of such methods can be found in. [1][2][3][4] It is often too restrictive to require that grid nodes should be collocated at subdomain interfaces. A discretization that uses grids whose nodes are not collocated at the subdomain interfaces is called nonconforming (see for example Figure 1).…”