ON FINITE DIFFERENCE SCHEMES FOR THE 3-D WAVE EQUATION USING NON-CARTESIAN GRIDS

In this paper, we investigate finite difference schemes for the 3-D wave equation using 27-point stencils on the cubic lattice, a 13-point stencil on the face-centered cubic (FCC) lattice, and a 9-point stencil on the body-centered cubic (BCC) lattice. The tiling of the wavenumber space for nonCartesian grids is considered in order to analyse numerical dispersion. Schemes are compared for computational efficiency in terms of minimising numerical wave speed error. It is shown that the 13-point scheme on the FCC lattice is more computationally efficient than 27-point schemes on the cubic lattice when less than 8% error in the wave speed is desired.

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