Calculation of Fluid Flows With Staggered and Nonstaggered Curvilinear Nonorthogonal Grids-the Theory

Two finite-volume methods for discretization of conservation equations in three dimensions when using curvilinear nonorthogonal coordinates are presented, and both necessary coordinate and velocity transformations are given by tensor calculus. One of the methods is based on the nonstaggered grid arrangement and uses Cartesian velocity components as dependent variables in the momentum equations. Rhie and Chow interpolation is used to get a good coupling between pressure and velocity. In the other method, a staggered grid arrangement together with physical covariant velocity projections is used in a locally fixed coordinate system. Both methods are based on the SIMPLE algorithm.