Stable and accurate wave-propagation in discontinuous media. (English) Zbl 1151.65070
Summary: 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) subdomain 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.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35L05 | Wave equation |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
Keywords:
high-order finite difference methods; unstructured finite volume method; wave equation; stability; discontinuous media; complex geometries; numerical examplesReferences:
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