NEW, STRONGLY CONSERVATIVE FINITE-VOLUME FORMULATION FOR FLUID-FLOWS IN IRREGULAR GEOMETRIES USING CONTRAVARIANT VELOCITY COMPONENTS .1. THEORY

A strongly conservative finite-volume procedure is presented for flows in complex geometries. The technique is based on a complete transform ation of the governing equations, and physical velocity components, ra ther than the traditionally used Cartesian velocity components, are us ed as primitive variables. It was found that projecting the discretize d vector transport equation in the direction of the covariant base vec tors eliminated two substantial difficulties associated with flows in complex geometries. These difficulties stem from the presence of cross -pressure gradient terms and the need for a transformation between the different types of curvilinear velocity components in the mass conser vation equation. It is shown that the present formulation ensures that the computational scheme is diagonally dominant. It was found that pa rtially implicit treatment of nonorthogonal diffusion terms improved t he convergence rate primarily for high-cell-Reynolds-number values. Fo r nonstaggered grids, a new solution procedure that combines features of both the SIMPLER and PlSO algorithms is proposed.