Efficient and accurate numerical simulation of acoustic wave propagation in a 2D heterogeneous media

摘要

In this paper, a compact fourth-order finite difference scheme is derived to solve the 2D acoustic wave equation in heterogenous media. The Pade approximation is used to obtain fourth-order accuracy in both temporal and spatial dimensions, and the alternating direction implicit (ADI) technique is used to reduce the computational cost. Due to the non-constant wave velocity, the conventional ADI method is hard to implement as the algebraic manipulation cannot be used here. A novel numerical strategy is proposed in this work so that the compact scheme still maintains fourth-order accuracy in time and space. The fourth-order convergence order was firstly proved by theoretical error analysis, then was confirmed by numerical examples. It was shown that the proposed method is conditionally stable with a Courant-Friedrichs-Lewy (CFL) condition that is comparable to other existing finite difference schemes. Several numerical examples were solved to demonstrate the efficiency and accuracy of the new algorithm. (C) 2017 Elsevier Inc. All rights reserved.