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A 3D finite element multigrid solver for the Euler equations
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1992
Year
Numerical AnalysisEngineeringFluid MechanicsMechanical EngineeringComputer-aided DesignStructural OptimizationComputational MechanicsMesh OptimizationCompressible FlowSteady StateNumerical SimulationEuler EquationsBoundary Element MethodMethod Of Fundamental SolutionIncompressible FlowUnstructured Mesh GenerationLow StorageMultiphase FlowNumerical Method For Partial Differential EquationFinite Element MethodFluid-structure InteractionCentered SchemeMultiscale Modeling
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 centered scheme with the explicit addition of a high accuracy artificial viscosity and the solution is advanced to steady state by means of a multistage timestepping 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.