Symmetrization of Coefficient Matrix for Two-Phase Media Wave Equation and its SBP-SAT Difference Simulation

Symmetrization of the coefficient matrix of the wave equation is an effective method to integrate different types of wave equations and reduce the difficulty of wave propagation simulation. It has been successfully applied to acoustic wave equations and elastic wave equations in isotropic and anisotropic media. In this paper, the symmetric format of the coefficient matrix of the two-term medium wave equation will be derived. Subsequently, a multi-axis perfectly matched layer is introduced, and the upwind scheme SBP-SAT difference method is used to discretize the wave equation, and the stability is evaluated by the energy method. Numerical simulations show that the proposed discrete framework has the characteristics of high integration, good stability and strong expansibility. In addition, the method in this paper can stably simulate wave propagation in curved domains and reduce its implementation cost, indicating that the symmetrization method of the coefficient matrix of the wave equation and its discrete framework have broad application prospects in the field of wave propagation simulation.