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A High Accuracy Local One‐Dimensional Explicit Compact Scheme for the 2D Acoustic Wave Equation

Author

Listed:
  • Mengling Wu
  • Yunzhi Jiang
  • Yongbin Ge

Abstract

In this paper, we develop a highly accurate and efficient finite difference scheme for solving the two‐dimensional (2D) wave equation. Based on the local one‐dimensional (LOD) method and Padé difference approximation, a fourth‐order accuracy explicit compact difference scheme is proposed. Then, the Fourier analysis method is used to analyze the stability of the scheme, which shows that the new scheme is conditionally stable and the Courant‐Friedrichs‐Lewy (CFL) condition is superior to most existing methods of equivalent order of accuracy in the literature. Finally, numerical experiments demonstrate the high accuracy, stability, and efficiency of the proposed method.

Suggested Citation

  • Mengling Wu & Yunzhi Jiang & Yongbin Ge, 2022. "A High Accuracy Local One‐Dimensional Explicit Compact Scheme for the 2D Acoustic Wave Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:9743699
    DOI: 10.1155/2022/9743699
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    References listed on IDEAS

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    1. Portillo, A.M., 2018. "High-order full discretization for anisotropic wave equations," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 1-16.
    2. Liao, Wenyuan & Yong, Peng & Dastour, Hatef & Huang, Jianping, 2018. "Efficient and accurate numerical simulation of acoustic wave propagation in a 2D heterogeneous media," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 385-400.
    3. Deng, Dingwen & Liang, Dong, 2018. "The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 188-209.
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