Multigrid and upwind viscous flow solver on three-dimensional overlapped and embedded grids

A computationally efficient method is presented for solving the three-dimensional governing equations of the viscous compressible flows about complex configurations with geometrically nonsimilar components. The physical domain is decomposed into regions for which the grid generation is relatively simple and virtually without significant restrictions. The Navier-Stokes equations are solved by an implicit, upwind, finite-volume scheme. The convergence is accelerated by a multigrid algorithm despite the holes created in the computational domain by the overlapped grids, which are completely or partially embedded within one another. The block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the existence of such holes. The method is tested through two demonstrative csises. The solution for a supersonic flow past a blunt-nose cylinder at a high angle of attack is obtained using a C-O grid embedded in a global Cartesian grid. This solution is successfully compared with the one obtained using a single C-O grid and the experimental data. Then, supersonic interference flows past an ogive-nose cylinder in the close proximity of a flat plate are solved using overlapped and topologically nonsimilar but simple grids.