An artificial compressibility method for incompressible flows

An artificial compressibility method characterized by the pressure-based al gorithm is developed on a nonorthogonal collocated grid for incompressible fluid flow problems, using a cell-centered finite-volume approximation. Unl ike the traditional pseudo-compressibility concept, the continuity constrai nt is perturbed by the material derivative of pressure, the physical releva nce of which is to invoke matrix preconditionings. Tile approach provokes d ensity perturbations, assisting the transformation between primitive and co nservative variables. To account for the flow directionality in the upwindi ng, a rotational matrix is introduced to evaluate the convective flux. A ra tional means of reducing excessive numerical dissipation inherent in the pr essure-velocity coupling is contrived which has the expedience of greater f lexibility and increased accuracy in a way similar to the MUSCL approach. N umerical experiments in reference to a few laminar flows demonstrate that t he overall artifacts expedite enhanced robustness and anticipated oscillati on damping properties adhering to the factored pseudo-time integration proc edure.