A computational scheme in generalized coordinates for viscous incompressible flows

This paper presents a computational scheme suitable for analyzing viscous incompressible flows in generalized curvilinear coordinate system. The scheme is based on finite volume algorithm with an overlapping staggered grid. The pseudo-diffusive terms arising from the coordinate transformation are treated as source terms. The system of nonlinear algebraic equations is solved by a semi-implicit procedure based upon line-relaxation and a generalization of Patankar's pressure correction algorithm. Examples of the application of the algorithm to flow in convergent channels, developing flow in a U-bend, and flow past backward facing step, are given. In addition, the case of flow past backward facing step is analyzed in detail, and the computed flowfields are found to be in close agreement with previous experimental and numerical results for expansion ratio (defined as the ratio of step height to channel height) of 0.5. The results are summarized in the form of a correlation relating the primary separation length, Reynolds number and expansion ratio.