A modified numerical-flux-based discontinuous Galerkin method for 2D wave propagations in isotropic and anisotropic media

Abstract

We have developed a new discontinuous Galerkin (DG) method to solve the 2D seismic wave equations in isotropic and anisotropic media. This method uses a modified numerical flux that is based on a linear combination of the Godunov and the centered fluxes. A weighting factor is introduced in this modified numerical flux that is expected to be optimized to some extent. Through the investigations on the considerations of numerical stability, numerical dispersion, and dissipation errors, we develop a possible choice of optimal weighting factor. Several numerical experiments confirm the effectiveness of the proposed method. We evaluate a convergence test based on cosine wave propagation without the source term, which shows that the numerical errors in the modified flux-based DG method and the Godunov-flux-based method are quite similar. However, the improved computational efficiency of the modified flux over the Godunov flux can be demonstrated only at a small sampling rate. Then, we apply the proposed method to simulate the wavefields in acoustic, elastic, and anisotropic media. The numerical results show that the modified DG method produces small numerical dispersion and obtains results in good agreement with the reference solutions. Numerical wavefield simulations of the Marmousi model show that the proposed method also is suitable for the heterogeneous case.