Multigrid flow solutions in complex two‐dimensional geometries

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Abstract
A finite difference solution algorithm is described for use on two‐dimensional curvilinear meshes generated by the solution of the transformed Laplace equation. The efficiency of the algorithm is improved through the use of a full approximation scheme (FAS) multigrid algorithm using an extended pressure correction scheme as smoother. The multigrid algorithm is implemented as a fixed V‐cycle through the grid levels with a constant number of sweeps being performed at each grid level.The accuracy and efficiency of the numerical code are validated using comparisons of the flow over two backward step configurations. Results show close agreement with previous numerical predictions and experimental data. Using a standard Cartesian co‐ordinate flow solver, the multigrid efficiency obtainable in a rectangular system is shown to be reproducible in two‐dimensional body‐fitted curvilinear co‐ordinates. Comparisons with a standard one‐grid method show the multigrid method, on curvilinear meshes, to give reductions in CPU time of up to 93%.