Time-space domain dispersion reduction schemes in the uniform norm for the 2D acoustic wave equation

Abstract

Finite-difference (FD) methods for the wave equation are flexible, robust and easy to implement. However, they in general suffer from numerical dispersion. FD methods based on accuracy give good dispersion at low frequencies, but waves tend to disperse for higher wavenumbers. Moreover, waves in higher dimensions also suffer from dispersion errors in all propagation angles. In this work, we give a unified methodology to derive dispersion reduction FD schemes for the two dimensional acoustic wave equation. This new methodology would generate schemes that give the theoretical minimum dispersion error in the uniform norm. Stability criteria are discussed for the general scheme. We also motivate the equivalence of popular dispersion reduction methodology and theoretical numerical reduction methodology.