An improved simple method on a collocated grid

A pressure-based method characterized bl! the SIMPLE algorithm is developed on a nonorthogonal collocated grid for solving two-dimensional incompressible fluid flow problems, using a cell-centered finite-volume appl oxidation. 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 where 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 the pressure underrelaxation. Consequently, included benefits ale the use of larger Courant numbers, enhanced robustness, and improved overall damping properties of the unfactored pseudo-time integration procedure.