Stable and accurate wave-propagation in discontinuous media

Authors:
Ken Mattsson;Frank Ham;Gianluca Iaccarino
Affiliations:
Department of Information Technology, Uppsala University, MIC, Polacksbacken, 751 05 Uppsala, Sweden;Department of Information Technology, Uppsala University, MIC, Polacksbacken, 751 05 Uppsala, Sweden;Department of Information Technology, Uppsala University, MIC, Polacksbacken, 751 05 Uppsala, Sweden
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

A time stable discretization is derived for the second-order wave equation with discontinuous coefficients. The discontinuity corresponds to inhomogeneity in the underlying medium and is treated by splitting the domain. Each (homogeneous) sub domain is discretized using narrow-diagonal summation by parts operators and, then, patched to its neighbors by using a penalty method, leading to fully explicit time integration. This discretization yields a time stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension using high-order finite difference discretizations, and in three-dimensions using an unstructured finite volume discretization.