MULTIGRID STRATEGIES FOR VISCOUS-FLOW SOLVERS ON ANISOTROPIC UNSTRUCTURED MESHES

Unstructured multigrid techniques for relieving the stiffness associat ed with high-Reynolds number viscous flow simulations on extremely str etched grids are investigated. One approach consists of employing a se mi-coarsening or directional-coarsening technique, based on the direct ions of strong coupling within the mesh, in order to construct more op timal coarse grid levels. An alternate approach is developed which emp loys directional implicit smoothing with regular fully coarsened multi grid levels. The directional implicit smoothing is obtained by constru cting implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergen ce rates over the traditional explicit full-coarsening multigrid algor ithm. However, maximum benefits are achieved by combining the two appr oaches in a coupled manner into a single algorithm. An order of magnit ude increase in convergence rate over the traditional explicit full-co arsening algorithm is demonstrated, and convergence rates for high-Rey nolds number viscous hows which are independent of the grid aspect rat io are obtained. Further acceleration is provided by incorporating low -Mach-number preconditioning techniques, and a Newton-GMRES strategy w hich employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is docume nted through several example test cases. (C) 1998 Academic Press.