An Improved Simple Method on a Collocated Grid

A pressure-based method characterized by the SIMPLE algorithm is developed on a nonorthogonal collocated grid for solving two-dimensional incompressible fluid flow problems, using a cell-centered finite-volume approximation. The concept of artificial density is combined with the pressure Poisson equation that provokes density perturbations, assisting the transformation between primitive and conservative variables. A nonlinear explicit flux correction is utilized at the cell face in discretizing the continuity equation, which functions effectively in suppressing pressure oscillations. The pressure-correction equation principally consolidates a triplicate-time approach when the Courant number CFL > 1. A rotational matrix, accounting for the flow directionality in the upwinding, is introduced to evaluate the convective flux. The numerical experiments in reference to a few familiar laminar flows demonstrate that the entire contrivance executes a residual smoothing enhancement, facilitating an avoidance of ...