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

• Autores: Sambit Das, Wenyuan Liao, Anirudh Gupta
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 258, Nº 1, 2014, págs. 151-167
• Idioma: inglés
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• Resumen

  • 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 (ADI) technique and Padé 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 Padé approximation in both y and temporal dimensions while the non-compact stage is based on Padé 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.