High order finite difference methods for wave propagation in discontinuous media

Authors:
Ken Mattsson;Jan Nordström
Affiliations:
Center for Turbulence Research, Stanford University, Mechanical Engineering, Building 500, Room 500A, 488 Escondido Mall, Stanford, CA 94305-3035, United States;Department of Information Technology, Scientific Computing, Uppsala University, P.O. Box 337, 75105 Uppsala, Sweden and Department of Computational Physics, Division of System Technology, The Swed ...
Venue:
Journal of Computational Physics
Year:
2006

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Abstract

High order finite difference approximations are derived for the second order wave equation with discontinuous coefficients, on rectangular geometries. The discontinuity is treated by splitting the domain at the discontinuities in a multi block fashion. Each sub-domain is discretized with compact second derivative summation by parts operators and the blocks are patched together to a global domain using the projection method. This guarantees a conservative, strictly stable and high order accurate scheme. The analysis is verified by numerical simulations in one and two spatial dimensions.