Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods
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Authors
O'Reilly, Ossian
Nordstrom, Jan
Kozdon, Jeremy E.
Dunham, Eric M.
Subjects
elastic waves
earthquake
high order finite difference finite volume
summation-byparts
simultaneous approximation term
weak nonlinear boundary conditions
earthquake
high order finite difference finite volume
summation-byparts
simultaneous approximation term
weak nonlinear boundary conditions
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Date of Issue
2013-10
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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.
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Article
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Department
Applied Mathematics
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Linköping University Electronic Press, Report
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.