A parallel weighted Runge-Kutta discontinuous galerkin method for solving acousitc wave equations in 3D D'Alembert media on unstructured meshes

Discontinuous Galerkin method (DGM) is a widely used numerical algorithm. It has the advantages of high accuracy, flexibility in dealing with boundary conditions, easy parallelism, and small numerical dispersion when solving seismic wave equations. In order to satisfy the numerical simulation for accuracy and complex geological structures, in this paper, we suggest a weighted Runge-Kutta discontinuous Galerkin (WRKDG) method for solving the acoustic wave equation in three-dimensional (3D) medium with strong attenuation D' Alembert medium on unstructured meshes. The numerical scheme is derived in detail, and the general numerical stability conditions are presented based on the theory of ordinary differential equations. The numerical dispersion and dissipation of WRKDG method are also investigated for the first time, including the influence of dissipation parameters on the analysis results. In addition, we carry out a convergence test of this method, and analyze the parallel speedup ratio of the WRKDG method in 3D case. The results show that the 3D WRKDG method has good parallel capabilities. Finally, we present several numerical examples in complex media with strong attenuation, including an homogeneous model, an irregular geometric model, and the heterogeneous Marmousi model. The results show that the method is not only accurate and in good agreement with the analytical solution, but also can effectively simulate the acoustic wave field in irregular model including sphere and heterogeneous Marmousi model. Finally, we present several numerical examples. Numerical results further verify the correctness and effectiveness of the 3D WRKDG method in solving the scalar wave equation in D' Alembert medium, and they clearly show the wave propagation characteristics of this strong attenuation medium.