Multigrid calculation of fluid flows in complex 3D geometries using curvilinear grids

A multigrid method is developed for numerical simulation of fluid hows in general curvilinear grids. The numerical formulation is based on a recently developed finite volume method for flows in complex geometries which uses a staggered grid system, grid-oriented velocity unknowns, a direct discretization technique and a coupled solution procedure. The present study reveals that the discrete governing equations on coarse and fine grids can become inconsistent in certain curvilinear grids due to complex flow boundaries, thus reducing the efficiency of the multigrid algorithm. A new method is proposed to solve this problem. Computations using grids with both significant non-orthogonality and strong curvature were carried out and the results show that the developed multigrid algorithm is very efficient: the computation can be hundreds of magnitudes faster when compared with the single-grid method. Comparison between the proposed multigrid method and conventional multigrid methods shows that the proposed formulation for the coarse-grid equations can substantially improve the multigrid efficiency for certain configurations and Reynolds numbers. (Copyright (C) 1996 Elsevier Science Ltd)