Integrated Fast and High Accuracy Computation of Convection Diffusion Equations Using Multiscale Multigrid Method
نویسندگان
چکیده
We present an explicit sixth order compact finite difference scheme for fast high accuracy numerical solutions of the two dimensional convection diffusion equation with variable coefficients. The sixth order scheme is based on the well-known fourth order compact scheme, the Richardson extrapolation technique, and an operator interpolation scheme. For a particular implementation, we use multiscale multigrid method to compute the fourth order solutions on both the coarse grid and the fine grid. Then an operator interpolation scheme combined with the Richardson extrapolation technique is used to compute a sixth order accurate fine grid solution. We compare the computed accuracy and the implementation cost of the new scheme with the standard nine-point fourth order compact scheme and Sun-Zhang’s sixth order method. Two convection diffusion problems are solved numerically to validate our proposed sixth order scheme.
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