Staggered Grid with Collocated Grid Points of Velocities for Modeling Propagation of Elastic Waves in Anisotropic Solids by Finite-Difference Time Domain Method

Abstract

A staggered grid for velocity–stress formulation is presented for modeling elastic waves in anisotropic solids by the finite-difference time domain method. To simply impose boundary conditions on numerical models, our grid is derived by applying a finite integration technique to a single control volume satisfying Newton's law instead of interleaved control volumes for conventional staggered grids. Computed results for the numerical dispersions of the new grid for propagating vertically polarized shear and longitudinal waves in an isotropic solid show that the numerical dispersions of the new grid can be suppressed to the same levels as those of the conventional staggered grids by using a third-degree bi-polynomial interpolation.