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High order semi-implicit weighted compact nonlinear scheme for viscous Burgers’ equations

Author

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  • Jiang, Yanqun
  • Chen, Xun
  • Fan, Rong
  • Zhang, Xu

Abstract

This paper develops a high order semi-implicit weighted compact nonlinear scheme (WCNS) for one- and two-dimensional viscous Burgers’ equations. This semi-implicit WCNS combines a fifth-order WCNS with a third-order implicit-explicit Runge–Kutta (IMEX-RK) time-stepping method. The advection terms of viscous Burgers’ equations are treated explicitly, while the viscosity terms are treated implicitly. Stability analysis shows that the CFL condition of the semi-implicit WCNS is controlled only by the advection terms. Compared to the explicit time-stepping method, the semi-implicit method has the advantage in terms of computational efficiency. Numerical results validate the accuracy and efficiency of the semi-implicit WCNS. This method can also solve viscous Burgers’ equations with large Reynolds numbers and has high-resolution shock-capturing ability.

Suggested Citation

  • Jiang, Yanqun & Chen, Xun & Fan, Rong & Zhang, Xu, 2021. "High order semi-implicit weighted compact nonlinear scheme for viscous Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 607-621.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:607-621
    DOI: 10.1016/j.matcom.2021.06.006
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    Cited by:

    1. Zhang, Xu & Jiang, Yanqun & Hu, Yinggang & Chen, Xun, 2022. "High-order implicit weighted compact nonlinear scheme for nonlinear coupled viscous Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 151-165.

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