Imaging the earth's interior
A modified equation approach to constructing fourth order methods for acoustic wave propagation
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Numerical Analysis
A three-point combined compact difference scheme
Journal of Computational Physics
Journal of Computational Physics
Short note: A high-order Padé ADI method for unsteady convection-diffusion equations
Journal of Computational Physics
High-order schemes for acoustic waveform simulation
Applied Numerical Mathematics
Journal of Computational Physics
A new time-space domain high-order finite-difference method for the acoustic wave equation
Journal of Computational Physics
A new high accuracy locally one-dimensional scheme for the wave equation
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
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 Pade 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 Pade approximation in both y and temporal dimensions while the non-compact stage is based on Pade 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.