A Three Dimensional Finite Volume Method in Curvilinear Coordinates for Complex Geometries: Formulation and Analysis

A strongly conservative finite volume formulation for complex geometries in three-dimensions using a complete transformation of the governing equations on a nonstaggered grid is presented. This method retains its conservative character at the scalar discretization level. The use of physical contravariant components as dependent variables eliminates the need for any transformation to calculate the cell face mass fluxes. A partially implicit treatment of the nonorthogonal diffusion terms is used to enhance the diagonal dominance of the scheme. This is an extension of the method proposed by Sharatchandra (1994). The method is then tested for two test problems for which analytical solutions are available and an error analysis is performed.