A Weighted Runge–Kutta Discontinuous Galerkin Method for Wavefield Modelling

he, xijun ; yang, dinghui ; wu, hao;

In this paper, we propose a weighted Runge–Kutta (RK) discontinuous Galerkin (WRKDG) method for wave field modelling. For this method, we first transform these is mic wave equations in 2-D heterogeneous anisotropic media in to a first-order hyperbolicsystem, and then combine the discontinuous Galerkin method (DGM) with a weighted RK time discretization. The time discretization is based on an implicit diagonal RK method and an explicit technique, which changes the implicit RK method into an explicit one. In addition, we introduce a weighting factor in the process. Linear and quadratic polynomials for spatial basis functions are typically employed. We investigate the properties of the method in great detail, including the stability criteria and numerical dispersion relations for solving the 2-D acoustic equations. Our analysis indicates that the stability condition for the WRKDG method is more relaxed compared with the classic total variation diminishing (TVD) RK discontinuous Galerkin (RKDG) method,resultingina1.7times superiority for P1 element and is about a sefficient as TVD RKDG method for P2 element in computational efficiency. We also demonstrate that the WRKDG method can suppress numerical dispersion more efficiently than the staggered-grid (SG) method on the same grid. The WRKDG method is applied to simulate the wavefields in a large velocity contrast model, a 2-D homogeneous transversely isotropic (TI) model, a fluid-filled fracture model, and a 2-D SEG/EAGE salt dome model. Regular rectangular and irregular triangular elements are used. The numerical results show that the WRKDG method can effectively suppress numerical dispersion and provide accurate information on the wavefield on a coarse mesh. Therefore, the method evidently reduces the scale of the problem and increases computational efficiency. In addition, promising numerical tests show that the WRKDG method combines well with split perfectly matched layer boundary conditions.