Dispersion-corrected explicit integration of the wave equation
A simple dispersion correction is introduced into the centered difference explicit time integration scheme for wave propagation problems. The extra term introduces a change of 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 to apply 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.
wave equation explicit time integration numerical dispersion central differences