AN IMPLICIT NUMERICAL SCHEME FOR THE SIMULATION OF INTERNAL VISCOUS-FLOW ON UNSTRUCTURED GRIDS

The development of a cell-centered unstructured grid solution for the two-dimensional Navier-Stokes equations is described. A finite-volume approach is used to discretize the conservation law form of the compre ssible dow equations written in terms of primitive variables. Temporal preconditioning is employed so that low Mach number Rows can be solve d economically. The equations are marched in time using either an impl icit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient-like method. A four color scheme is employed to vectorize th e block Gauss-Seidel relaxation procedure. This increases the memory r equirements minimally and decreases the computer time spent solving th e resulting system of equations substantially. A factor of 7.6 speedup in the matrix solver is typical for the viscous equations. The grids are generated based on the method of Delaunay triangulation. Numerical results are obtained for inviscid flow over a bump in a channel at su bsonic and transonic conditions for validation with structured solvers . Viscous results are computed For developing flow in a channel, a sym metric sudden expansion, periodic tandem cylinders in a cross-flow, an d a four-port valve. Comparisons are made with available results obtai ned by other investigators. Published by Elsevier Science Ltd.