General rectangular grid based time-space domain high-order finite-difference methods for modeling scalar wave propagation

Abstract

We develop the general rectangular grid discretization based time-space domain high-order staggered-grid finite-difference (SGFD) methods for modeling three-dimension (3D) scalar wave propagation. The proposed two high-order SGFD schemes can achieve the arbitrary even-order accuracy in space, and the fourth- and sixth-order accuracies in time, respectively. We derive the analytical expression of the high-order FD coefficients based on a general rectangular grid discretization with different grid spacing in all axial directions. The general rectangular grid discretization makes our time-space domain SGFD schemes more flexible than the existing ones developed on the cubic grid with the same grid spacing in the axial directions. Theoretical analysis indicates that our time-space domain SGFD schemes have a better stability and a higher accuracy than the traditional temporal second-order SGFD scheme. Our time-space domain SGFD schemes allow larger time steps than the traditional SGFD scheme for attaining a similar accuracy, and thus are more efficient. Numerical example further confirms the superior accuracy, stability and efficiency of our time-space domain SGFD schemes.