Runge-Kutta discontinuous Galerkin method for solving wave equations in 2D isotropic and anisotropic poroelastic media at low frequencies
A Runge-Kutta discontinuous Galerkin (RKDG) method for solving wave equations in isotropic and anisotropic poroelastic media at low frequencies is introduced. 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 (DGM) 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 the proposed method in isotropic and anisotropic poroelastic media. Comparisons of seismic responses with the finite-difference method (FDM) 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 the proposed method can deal with complex wave propagation. Therefore, the simulation results show that the RKDG method is an accurate and stable method for solving Biot’s equations.