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Dispersion-corrected explicit integration of the wave equation. (English) Zbl 1009.76054
Summary: We introduce a dispersion correction into a centered difference explicit time integration scheme for wave propagation problems. The extra term introduces a change in the wave speed, depending on local wave characteristics. A rigorous theoretical analysis is provided for the scalar wave equation on a regular mesh, and a notable improvement in the ability to conserve wave fronts is demonstrated by two numerical examples. The correction is reinterpreted by application to a typical finite element formulation in terms of mass and stiffness matrices, resulting in a general dispersion correction of the explicit centered difference time integration algorithm for acoustic and elastic wave propagation problems.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
74J10 Bulk waves in solid mechanics
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