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

In this paper, a compact fourth-order finite difference scheme is derived to solve the 2D acoustic wave equation in heterogenous media. The Padé 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.