Runge-Kutta discontinuous Galerkin method for solving wave equations in 2D isotropic and anisotropic poroelastic media at low frequencies

Abstract

We have developed a Runge-Kutta discontinuous Galerkin (RKDG) method for solving wave equations in isotropic and anisotropic poroelastic media at low frequencies. First, the 2D Biot’s two-phase equations are transformed into a first-order system with dissipation. Then, the system is discretized by using the discontinuous Galerkin method with a third-order Runge-Kutta time discretization. The numerical stability conditions for solving porous equations are also investigated. We test several examples to validate our method in isotropic and anisotropic poroelastic media. Comparisons of seismic responses with the finite-difference method on fine grids show the correctness of this method. Moreover, the numerical results indicate that the RKDG method can provide clear fast P-, slow P-, and S-waves for anisotropic poroelastic media on coarse meshes. Also, a two-layer porous model, a poroelastic-elastic model with horizontal interface, and an isotropic-anisotropic poroelastic model with sinusoidal interface demonstrate that our method can deal with complex wave propagation. Therefore, the simulation results show that RKDG is an accurate and stable method for solving Biot’s equations.