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A class of compact finite difference schemes for solving the 2D and 3D Burgers’ equations

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  • Yang, Xiaojia
  • Ge, Yongbin
  • Lan, Bin

Abstract

In this paper, a class of two-level high-order compact finite difference implicit schemes are proposed for solving the Burgers’ equations. Firstly, based on the fourth-order compact finite difference schemes for spatial derivatives and the truncation error remainder correction method for temporal derivative, the high-order compact (HOC) difference method is introduced for solving the one-dimensional (1D) Burgers’ equation. At the same time, the stability of the scheme is analyzed by using the Fourier analysis method. Because only three grid points are involved in each time level. The Thomas algorithm can be directly used to solve the tridiagonal linear system. Then, this method is extended to solve the two-dimensional (2D) and three-dimensional (3D) coupled Burgers’ equations. Finally, numerical experiments are conducted to verify the accuracy and the reliability of the present schemes.

Suggested Citation

  • Yang, Xiaojia & Ge, Yongbin & Lan, Bin, 2021. "A class of compact finite difference schemes for solving the 2D and 3D Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 510-534.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:510-534
    DOI: 10.1016/j.matcom.2021.01.009
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    References listed on IDEAS

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    1. Hammad, D.A. & El-Azab, M.S., 2015. "2N order compact finite difference scheme with collocation method for solving the generalized Burger’s–Huxley and Burger’s–Fisher equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 296-311.
    2. Zhanlav, T. & Chuluunbaatar, O. & Ulziibayar, V., 2015. "Higher-order accurate numerical solution of unsteady Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 701-707.
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