A semi-coarsening strategy for unstructured multigrid based on agglomeration

✍ Scribed by Jerome Francescatto; Alain Dervieux

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 481 KB
• Volume: 26
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(19980430)26:8<927::aid-fld679>3.0.co;2-0

✦ Synopsis

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.