Implicit time-accurate solutions on unstructured dynamic grids
Copyright policy )Implicit time-accurate solutions on unstructured dynamic grids
Summary: We use an unstructured multigrid algorithm as an iterative solution procedure for the discrete equations arising from an implicit time discretizatin of the unsteady Euler equations on tetrahedral grids. To calculate unsteady flows due to oscillating boundaries, a novel grid movement algorithm is introduced in which an elliptic equation with a nonlinear diffusion coefficient is used to define the displacements of interior grid nodes. This allows large grid displacements to be calculated in a single step. The multigrid technique uses an edge-collapsing algorithm to generate a sequence of grids, and a pseudo-time-stepping smoother. On the coarser grids, no grid motion is used. Instead, surface normals are rotated consistently and transfer/interpolation weights are based on the time-averaged grid co-ordinates. A two-dimensional NACA 0012 test case is used to validate the programme. Three-dimensional results are presented for the M6 wing and a full aircraft configuration.
- University of Oxford United Kingdom
multigrid technique, tetrahedral grids, pseudo-time-stepping smoother, M6 wing, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, edge-collapsing algorithm, Finite difference methods applied to problems in fluid mechanics, iterative procedure, nonlinear diffusion coefficient, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, unsteady Euler equations, NACA 0012
multigrid technique, tetrahedral grids, pseudo-time-stepping smoother, M6 wing, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, edge-collapsing algorithm, Finite difference methods applied to problems in fluid mechanics, iterative procedure, nonlinear diffusion coefficient, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, unsteady Euler equations, NACA 0012
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