Abstract
A nonlinear multigrid method is developed for solving the three-dimensional Navier-Stokes equations in conjunction with the artificial compressibility formulation. The method is based on the full multigrid (FMG) - full approximation storage (FAS) - algorithm and is realized via an "unsteady-type" procedure, according to which the equations are not solved exactly on the coarsest grid, but some pseudo-time iterations are performed on the finer grids and some on the coarsest grid. The multigrid method is implemented in conjunction with a third-order upwind characteristics-based scheme for the discretization of the convection terms, and the fourth-order Runge-Kutta scheme for time integration. The performance of the method is investigated for three-dimensional flows in straight and curved channels as well as flow in a cubic cavity. The multigrid acceleration is assessed in contrast to the single-grid and mesh-sequencing algorithms. The effects of various multigrid components on the convergence acceleration, such as prolongation operators, as well as pre- and postrelaxation iterations, are also investigated.
Original language | English |
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Pages (from-to) | 301-321 |
Number of pages | 21 |
Journal | Journal of Computational Physics |
Volume | 146 |
Issue number | 1 |
DOIs | |
Publication status | Published - 10 Oct 1998 |
Externally published | Yes |
Keywords
- Artificial compressibility
- Multigrid
- Navier-Stokes equations
- Upwind schemes