A novel stability-improved discontinuous Galerkin method for wavefield simulation

Abstract

A novel stability-improved DG method is proposed for solving wave equations. It is termed the stabilized weighted Runge–Kutta discontinuous Galerkin method. We adopt the symmetric interior penalty Galerkin (SIPG) scheme for spatial discretization. For temporal discretization, we apply the stabilized weighted Runge–Kutta method proposed in this work. Stability analysis of the proposed scheme is carried out for the acoustic wave equation on rectangular meshes, demonstrating that the maximum allowable CFL number of the present approach is nearly 1.8 times that of the conventional third-order Runge–Kutta SIPG method. This indicates a significant stability improvement, enabling larger and more stable time steps in wavefield simulations. Compared with the conventional RKDG scheme, our method exhibits lower numerical dispersion for P1–P3 elements. Although the numerical dispersion increases slightly for P4 and P5 elements, the method still performs well. Several typical models are adopted for wavefield simulation. Numerical examples demonstrate the advantages of the stabilized WRKDG method. This method incorporates the discontinuous Galerkin scheme alongside efficient time integration techniques. The new formulation effectively suppresses numerical dispersion and shortens wavefield simulation time.