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Time compact difference methods for wave propagation in discontinuous media. (English) Zbl 1077.65092

Summary: B. Gustafsson and E. Mossberg [SIAM J. Sci. Comput. 26, No. 1, 259–271 (2004; Zbl 1075.65112)] constructed a fourth order one-step method for the solution of wave propagation problems. The method is based on the first order system form of the partial differential equation and uses a staggered grid both in space and time. The method was also applied with good results to a problem with discontinuous coefficients without using any special procedure across the discontinuity.
We analyze a model problem from acoustics and demonstrate the theoretical foundation for this behavior. Furthermore, we present more detailed numerical experiments which confirm the theoretical results.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
76Q05 Hydro- and aero-acoustics
76M20 Finite difference methods applied to problems in fluid mechanics

Citations:

Zbl 1075.65112
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