An artificial compressibility method for viscous incompressible and low Mach number flows

What is it about?

Within the framework of the pressure-based algorithm, an artificial compressibility method is developed on a non-orthogonal grid for incompressible and low Mach number fluid flow problems, using cell centered finite-volume approximation. Resorting to the traditional pseudo-compressibility concept, the continuity constraint is perturbed by the time 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. A dual-dissipation scheme for the pressure–velocity coupling is contrived, which has the expediences of greater flexibility and increased accuracy in a way similar to the monotone upstream-centered schemes for conservation laws approach. To account for the flow directionality in the upwinding, a rotational matrix is introduced to evaluate the convective flux. Numerical experiments in reference to a few well-documented laminar flows demonstrate that the entire contrivance expedites enhanced robustness and improved overall damping properties of the factored pseudo-time integration procedure.

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