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Implicit time‒accurate solutions on unstructured dynamic grids
Author(s) -
Crumpton P. I.,
Giles M. B.
Publication year - 1997
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19971215)25:11<1285::aid-fld607>3.0.co;2-m
Subject(s) - multigrid method , discretization , interpolation (computer graphics) , unstructured grid , grid , euler equations , displacement (psychology) , algorithm , mesh generation , surface (topology) , mathematics , computer science , geometry , mathematical analysis , partial differential equation , motion (physics) , finite element method , physics , psychology , artificial intelligence , psychotherapist , thermodynamics
Abstract In this paper an unstructured multigrid algorithm is used as an iterative solution procedure for the discrete equations arising from an implicit time discretization 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 non‒linear diffusion coefficient is used to define the displacement 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 2D NACA0012 test case is used to validate the programme. 3D results are presented for the M6 wing and a full aircraft configuration. © 1997 John Wiley & Sons, Ltd.