Acoustic wave propagation in complicated geometries and heterogeneous media. (English) Zbl 1306.65247
The authors’ propose finite difference discretizations for the acoustic wave equation in complicated geometries and heterogeneous media. Particular emphasis is placed on the accurate treatment of interfaces at which the underlying media parameters have jump discontinuities. Discontinuous media are treated by subdividing the domain into blocks with continuous media. The equation on each block is then discretized with finite difference operators satisfying a summation-by-parts property and patched together via the simultaneous approximation term method. The energy method is used to estimate a semi-norm of the numerical solution in terms of data, showing that the discretization is stable. Numerical experiments in two and three spatial dimensions verify the accuracy and stability properties of the schemes.
Reviewer: Qin Meng Zhao (Beijing)
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35L05 | Wave equation |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
acoustic wave equation; heterogeneous media; Curvilinear grids; high-order methods; strong stability; energy estimates; finite difference; energy method; numerical experimentSoftware:
OASESReferences:
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