AN ARTIFICIAL COMPRESSIBILITY METHOD FOR INCOMPRESSIBLE FLOWS

Abstract

An artificial compressibility method characterized by the pressure-based algorithm is developed on a nonorthogonal collocated grid for incompressible fluid flow problems, using a cell-centered finite-volume approximation. Unlike the traditional pseudo-compressibility concept, the continuity constraint is perturbed by the material derivative of pressure, the physical relevance of which is to invoke matrix preconditionings. The approach provokes density perturbations, assisting the transformation between primitive and conservative variables. To account for the flow directionality in the upwinding, a rotational matrix is introduced to evaluate the convective flux. A rational means of reducing excessive numerical dissipation inherent in the pressure–velocity coupling is contrived which has the expedience of greater flexibility and increased accuracy in a way similar to the MUSCL approach. Numerical experiments in reference to a few laminar flows demonstrate that the overall artifacts expedite enhanced robustness and anticipated oscillation damping properties adhering to the factored pseudo-time integration procedure.