An efficient poroelastic wave simulation based on discontinuous grid and nonuniform time step

The existence of slow P wave, in addition to fast P wave and S wave, makes it tricky for grid-based numerical simulation methods to conduct poroelastic wave modeling. The grid spacing has to be fine enough to capture the slow P wave since the velocity of slow P wave is much smaller than that of the other two waves. Dense space and time steps significantly increase the computation cost. In this study, we propose a poroelastic finite-difference simulation method that combines discontinuous curvilinear collocated-grid and non-uniform time step Runge-Kutta scheme. Only the space and time steps for the areas near interfaces, where the contribution of slow P wave is non-negligible, are refined in an effort to speed up the computation. The refined space step is determined by the velocity of slow P wave, while the coarse space step is determined by the velocity of shear wave. The coarse and refined time steps are set according to the non-uniform time step Runge-Kutta scheme, which is derived with Taylor expansion and avoids interpolation or extrapolation for communication between different time levels. This scheme helps maintain fourth-order accuracy in the whole domain. The accuracy and efficiency of the proposed method are verified by numerical tests. Compared with the conventional curvilinear collocated-grid finite-difference method that uses a uniform space grid as well as a uniform time step, the computation efficiency is improved significantly and the computation time can be saved by more than 80%.