Stability Analysis for Wave Simulation in 3D Poroelastic Media with the Staggered-Grid Method (Communications in Computational Physics, 2020)
In this paper, a new approach is proposed to analyse the stability of high-order staggered-grid finite difference schemes for the three-dimensional (3D) poroelastic wave propagation. The standard staggered-grid schemes with different order accuracy in space are constructed based on the first-order hyperbolic velocity-stress systemof the governing equations (i.e., Biot's equations). The new analysis method is basedon von Neumann analysis. The obtained 3D stability is an explicit restriction for timestep, which only depends on the coefficients of the difference operators and the material parameters of poroelastic media and so it can be computed easily. Moreover, theanalysis has good generality and can be applied directly to the staggered-grid schemesfor 3D elastic wave. Numerical computations with the perfectly matched layer in splitformation are implemented to illustrate the effectiveness of the schemes for 3D poroelastic wave propagation. The method in this paper can be expected to analyse thestability for other staggered-grid schemes.
Keywords: 3D; stability analysis; poroelastic media; wave propagation; staggered-grid.