An optimal nearly analytic splitting method for solving 2D acoustic wave equations

Abstract

In this article, we suggest a new optimal nearly analytic splitting (ONAS) method for 2D acoustic wave simulation. We first split 2D acoustic wave equation into the local one-dimensional (LOD) equations. Then we solve each of these equations over half of the time step used for the complete 2D wave equation using technique similar to the optimal nearly analytic discrete method (ONADM) for the 1D acoustic wave equation. We provide the theoretical study on the properties of the ONAS method, such as stability criteria, theoretical error, numerical error, and numerical dispersion. We also compare some acoustic modeling results of this method against those of the ONADM, the fourth-order nearly analytic symplectic partitioned Runge–Kutta (NSPRK) method, the fourth-order Lax–Wendroff correction (LWC) method. Theoretical analysis and numerical tests show that the ONAS method is fourth-order accurate in time and fourth-order accurate in space, and the ONAS method is much more effective than the fourth-order LWC, the fourth-order NSPRK and the ONADM in suppressing numerical dispersion. The new ONAS method theoretically preserves the symplectic geometry structure as time proceeds. Numerical results illustrate that the ONAS method has better numerical stability and long-term calculation capability as time proceeds than the ONADM