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

Published online by Cambridge University Press:  22 January 2015

Ossian O'Reilly ,
Jan Nordström ,
Jeremy E. Kozdon  and
Eric M. Dunham
Ossian O'Reilly*
Affiliation:
Department of Geophysics, Stanford University, CA 94305-2215, USA Department of Mathematics, Division of Computational Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Jan Nordström
Affiliation:
Department of Mathematics, Division of Computational Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Jeremy E. Kozdon
Affiliation:
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943-5216, USA
Eric M. Dunham
Affiliation:
Department of Geophysics, Stanford University, CA 94305-2215, USA Institute for Computational and Mathematical Engineering, Stanford University, CA 94305-4042, USA
*
*Email addresses: ooreilly@stanford.edu (O. O'Reilly), jan.nordstrom@liu.se (J. Nordström), jekozdon@nps.edu (J. E. Kozdon), edunham@stanford.edu (E. M. Dunham)
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Abstract

We couple a node-centered finite volume method to a high order finite difference method to simulate dynamic earthquake ruptures along nonplanar faults in two dimensions. The finite volume method is implemented on an unstructured mesh, providing the ability to handle complex geometries. The geometric complexities are limited to a small portion of the overall domain and elsewhere the high order finite difference method is used, enhancing efficiency. Both the finite volume and finite difference methods are in summation-by-parts form. Interface conditions coupling the numerical solution across physical interfaces like faults, and computational ones between structured and unstructured meshes, are enforced weakly using the simultaneous-approximation-term technique. The fault interface condition, or friction law, provides a nonlinear relation between fields on the two sides of the fault, and allows for the particle velocity field to be discontinuous across it. Stability is proved by deriving energy estimates; stability, accuracy, and efficiency of the hybrid method are confirmed with several computational experiments. The capabilities of the method are demonstrated by simulating an earthquake rupture propagating along the margins of a volcanic plug.

Keywords

35L0535L6535Q3565M0665M0865M1265Z05Elastic wavesearthquakehigh order finite difference finite volumesummation-by-partssimultaneous approximation termnonlinear boundary conditions
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 2 , February 2015 , pp. 337 - 370
Copyright
Copyright © Global Science Press Limited 2015 

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