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

*(English)*Zbl 1036.65082Summary: We present a fourth-order compact finite difference scheme on the face centered cubic 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.

##### MSC:

65N06 | Finite difference methods (BVP of PDE) |

35J25 | Second order elliptic equations, boundary value problems |

65F10 | Iterative methods for linear systems |

65N12 | Stability and convergence of numerical methods (BVP of PDE) |

65N55 | Multigrid methods; domain decomposition (BVP of PDE) |

65N15 | Error bounds (BVP of PDE) |