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 incompressi ble 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 cor rection is utilized at the cell face in discretizing the continuity, equati on, which functions effectively in suppressing pressure oscillations. The p ressure-correction equation principally consolidates a triplicate-time appr oach where the Courant number CFL >1, A rotational matrix, accounting for t he flow directionality in the upwinding, is introduced to evaluate the conv ective flux. The numerical experiments in reference to a few familiar lamin ar flows demonstrate that the entire contrivance executes a residual smooth ing enhancement, facilitating an avoidance of the pressure underrelaxation. Consequently, included benefits ale the use of larger Courant numbers, enh anced robustness, and improved overall damping properties of the unfactored pseudo-time integration procedure.