An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

The Navier-Stokesequations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A fmite-volurneapproach is used to discretizethe conservationlaw form ofthe compressibleflowequationswrittenin terms ofprimitivevariables.A preconditioningmatrix is added to the equations so that low Mach number flowscan be solvedeconomically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Ganss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speedup in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channd, a symmetric sudden expansion, periodic tan"Aero_sce Engineer, Member AIAA t Professor, Member AIAA °Copyright ©1994 by the American Institute of Aeronautics and astronautics, Inc. No copyright is _,serted in the UnitedStatesunderTitle17,U.S.code. The U.S.Governmeat hasa royalty freelicense toexercise allrightsunderthe cop_a4_ght _l_;_edhereinforGovernmentpurposes.An other rights are reserved by the copyright owner. dem cylindersin a cross-flow, and a four-portvalve. Comparisons aremade with availableresultsobtained by other investigators.