Mixed-grid finite-difference method for numerical simulation of 3D wave equation in the time-space domain

Conventional high-order and time-space domain high-order Finite-Difference (FD) methods have been widely used for 3D wave equation numerical simulation. These two FD schemes adopt the same FD stencil which only uses the axial grid nodes to construct the 3D Laplace difference operator, and the corresponding discrete difference wave equation can only reach 2nd-order accuracy. In this paper, we classify the off-axial grid nodes in the 3D Cartesian coordinate system into two categories: off-axial grid nodes in the coordinate plane and off-axial grid nodes outside the coordinate plane, and systematically derive the methods to construct the 3D Laplace difference operator with these two categories of off-axial grid nodes. Then a new kind of 3D mixed-grid FD scheme is proposed, which adopts a novel FD stencil combining the axial nodes and off-axial nodes to construct the Laplace difference operator and the FD coefficients are calculated based on the time-space domain dispersion relationship and Taylor expansion. The discrete difference wave equation derived from this new mixed-grid FD scheme can reach 4th-order, 6th-order and arbitrary even-order difference accuracy. So it can significantly improve the modeling accuracy comparing to conventional high-order and time-space domain high-order FD schemes, and also has better stability. Dispersion analysis shows comparing to conventional high-order and time-space domain high-order FD schemes, the mixed-grid FD scheme can more effectively suppress the numerical dispersion and weaken the numerical anisotropy to obtain higher modeling accuracy with almost the same computational efficiency, and it can obtain higher computational efficiency by adopting larger time interval with almost the same modeling accuracy. Numerical modeling experiments further verify the superiority of the mixed-grid FD scheme in improving the modeling accuracy and computational efficiency, and also demonstrate its universal applicability.