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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.

65M06Finite difference methods (IVP of PDE)
35L05Wave equation (hyperbolic PDE)
76Q05Hydro- and aero-acoustics
76M20Finite difference methods (fluid mechanics)