An efficient fourth-order low dispersive finite difference scheme for a 2-D acoustic wave equation

作者：Das Sambit; Liao Wenyuan^*; Gupta Anirudh

来源：Journal of Computational and Applied Mathematics, 2014, 258: 151-167.

DOI：10.1016/j.cam.2013.09.006

• Acoustic wave equation
• Finite difference
• Pade approximation
• Alternative direction implicit
• Numerical dispersion

In this paper, we propose an efficient fourth-order compact finite difference scheme with low numerical dispersion to solve the two-dimensional acoustic wave equation. Combined with the alternating direction implicit (ADD technique and Fade approximation, the standard second-order Finite difference scheme can be improved to fourth-order and solved as a sequence of one-dimensional problems with high computational efficiency. However such compact higher-order methods suffer from high numerical dispersion. To suppress numerical dispersion, the compact and non-compact stages are interlinked to produce a hybrid scheme, in which the compact stage is based on Fade approximation in both y and temporal dimensions while the non-compact stage is based on Fade approximation in y dimension only. Stability analysis shows that the new scheme is conditionally stable and superior to some existing methods in terms of the Courant-Friedrichs-Lewy (CFL) condition. The dispersion analysis shows that the new scheme has lower numerical dispersion in comparison to the existing compact ADI scheme and the higher-order locally one-dimensional (LOD) scheme. Three numerical examples are solved to demonstrate the accuracy and efficiency of the new method.

• 出版日期2014-3-1