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A family of fourth-order difference schemes on rotated grid for two-dimensional convection–diffusion equation

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  • Zhang, Jun
  • Kouatchou, Jules
  • Ge, Lixin

Abstract

We derive a family of fourth-order finite difference schemes on the rotated grid for the two-dimensional convection–diffusion equation with variable coefficients. In the case of constant convection coefficients, we present an analytic bound on the spectral radius of the line Jacobi’s iteration matrix in terms of the cell Reynolds numbers. Our analysis and numerical experiments show that the proposed schemes are stable and produce highly accurate solutions. Classical iterative methods with these schemes are convergent with large values of the convection coefficients. We also compare the fourth-order schemes with the nine point scheme obtained from the second-order central difference scheme after one step of cyclic reduction.

Suggested Citation

  • Zhang, Jun & Kouatchou, Jules & Ge, Lixin, 2002. "A family of fourth-order difference schemes on rotated grid for two-dimensional convection–diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(5), pages 413-429.
    • Handle: RePEc:eee:matcom:v:59:y:2002:i:5:p:413-429
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    1. Zhang, Jun & Ge, Lixin & Kouatchou, Jules, 2000. "A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 65-80.
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