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A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation

Author

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  • Sun, Haiwei
  • Kang, Ning
  • Zhang, Jun
  • Carlson, Eric S.

Abstract

We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. Numerical experiments are conducted to verify the fourth-order convergence rate of the derived discretization scheme and to show that the fourth-order compact difference scheme is computationally more efficient than the standard second-order central difference scheme.

Suggested Citation

  • Sun, Haiwei & Kang, Ning & Zhang, Jun & Carlson, Eric S., 2003. "A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(6), pages 651-661.
    • Handle: RePEc:eee:matcom:v:63:y:2003:i:6:p:651-661
    DOI: 10.1016/S0378-4754(03)00095-8
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    Cited by:

    1. Moreno, E. & Cruz-Hernández, P. & Hemmat, Z. & Mojab, A. & Michael, E.A., 2019. "Comparative study of grids based on the cubic crystal system for the FDTD solution of the wave equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 395-409.

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