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Multigrid solution of the 3-D compressible Euler equations on unstructured tetrahedral grids. (English) Zbl 0771.76042

Summary: A low storage, computationally efficient algorithm for the solution of the compressible Euler equations on unstructured tetrahedral meshes is developed. The algorithm takes the form of a centred scheme with the explicit addition of a high accuracy artificial viscosity, and the solution is advanced to steady state by means of a multi-stage time stepping method. The side based data structure which is employed enables a clear connection to be established between the proposed algorithm and upwind cell vertex schemes for unstructured meshes. The computational efficiency of the procedure is improved by incorporating an unstructured multigrid acceleration procedure. A number of flows of practical interest are analyzed to demonstrate the numerical performance of the proposed approach.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76H05 Transonic flows
76J20 Supersonic flows
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