Novel fully Implicit Collocated grid incompressible flow solver on unstructured meshes

Abstract

This article presents a novel implicit cell center finite volume scheme for solving two-dimensional incompressible steady state flows. A collocated approach has been employed considering its use in conjunction with unstructured meshes. The method inspired by the methodologies for compressible flow solvers is evolved to naturally accommodate several modules from such solvers. The explicit fluxes are computed to second order accuracy using the method of reconstruction. An inconsistent linearization is adopted for the implicit part which employs SGS sub-iterations. At the heart of the implicit procedure is obtaining an auxiliary velocity field, the divergence of which results in a Poisson equation for the pressure field, ensuring a divergence free velocity field resulting from the implicit iteration. The efficacy of the proposed method is demonstrated for several test problems, such as the flow past a Circular Cylinder, NACA 0012 airfoil and lid driven cavity.