Volume 17, Issue 2
Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

Ossian O'Reilly, Jan Nordström, Jeremy E. Kozdon & Eric M. Dunham

Commun. Comput. Phys., 17 (2015), pp. 337-370.

Published online: 2018-04

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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.

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@Article{CiCP-17-337, author = {Ossian O'Reilly , and Jan Nordström , and Jeremy E. Kozdon , and Eric M. Dunham , }, title = {Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {2}, pages = {337--370}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.111013.120914a}, url = {http://global-sci.org/intro/article_detail/cicp/10961.html} }
TY - JOUR T1 - Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods AU - Ossian O'Reilly , AU - Jan Nordström , AU - Jeremy E. Kozdon , AU - Eric M. Dunham , JO - Communications in Computational Physics VL - 2 SP - 337 EP - 370 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.111013.120914a UR - https://global-sci.org/intro/article_detail/cicp/10961.html KW - AB -

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.

Ossian O'Reilly, Jan Nordström, Jeremy E. Kozdon & Eric M. Dunham. (2020). Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods. Communications in Computational Physics. 17 (2). 337-370. doi:10.4208/cicp.111013.120914a
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