Abstract
A non linear multigrid method has been applied to the transonic potential flow equation discretized with a classical Galerkin Finite Element approach on a curvilinear body fitted mesh.
The generality of the finite element method with regard to the treatment of non uniform arbitrarily generated grids is preserved by introducing non uniform interpolation in the coarse grid finite element space for the prolongation of coarse grid functions. The residual restriction is also constructed in a way fully consistent with the finite element approximation resulting in a non uniform weighting of fine grid residuals.
Substantial convergence acceleration is obtained with standard line relaxation as smoothing step and an implementation of the Kutta-Youkowski condition in cascade configurations has been achieved without adverse effect on the convergence speed. Computational results are shown for isolated airfoil, channel and cascade geometries.
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References
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Deconinck, H., Hirsch, C. (1982). A multigrid finite element method for the transonic potential equation. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods. Lecture Notes in Mathematics, vol 960. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069935
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DOI: https://doi.org/10.1007/BFb0069935
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