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A semi‐coarsening strategy for unstructured multigrid based on agglomeration
Author(s) -
Francescatto Jerome,
Dervieux Alain
Publication year - 1998
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(19980430)26:8<927::aid-fld679>3.0.co;2-0
Subject(s) - multigrid method , euler equations , finite volume method , mathematics , poisson's equation , computational fluid dynamics , euler's formula , partial differential equation , computer science , mathematical optimization , mathematical analysis , physics , mechanics
Extending multigrid concepts to the calculation of complex compressible flow is usually not straightforward. This is especially true when non‐embedded grid hierarchies or volume agglomeration strategies are used to construct a gradation of unstructured grids. In this work, a multigrid method for solving second‐order PDE's on stretched unstructured triangulations is studied. The finite volume agglomeration multigrid technique originally developed for solving the Euler equations is used (M.‐H. Lallemand and A. Dervieux, in Multigrid Methods, Theory, Applications and Supercomputing , Marcel Dekker, 337–363 (1988)). First, a directional semi‐coarsening strategy based on Poisson's equation is proposed. The second‐order derivatives are approximated on each level by introducing a correction factor adapted to the semi‐coarsening strategy. Then, this method is applied to solve the Poisson equation. It is extended to the 2D Reynolds‐averaged Navier–Stokes equations with appropriate boundary treatment for low‐Reynolds number turbulent flows. © 1998 John Wiley & Sons, Ltd.