General Pressure Equation-Based Incompressible Flow Solver

Artificial compressibility method (ACM) in its various forms is widely used in numerical simulations of incompressible flows. Unlike the conventional methods, solving a pressure Poisson equation is not required in ACMs, making them computationally less expensive. The classical ACM is confined only to steady-state problems, and the extension to unsteady problems requires dual time-stepping. Apart from marching in actual time, additional inner iteration in pseudo-time is necessary for the dual time-stepping ACM, reducing their computational speed. Recent developments in artificial compressibility methods point towards single time-stepping versions such as entropically damped artificial compressibility (EDAC), general pressure equation (GPE). These algorithms neither involve numerically solving the pressure Poisson equation nor dual time-stepping and hence are computationally efficient. In this work, we developed an incompressible flow solver based on GPE and performed simulations with a few test cases. The unsteady test case of laminar Taylor–Green vortex problem indicates second-order convergence in both velocity and pressure, and the maximum error obtained is of the order of 10−4 for a grid of 64 × 64 at t = 1.0 s. The steady-state cases of laminar flow over flat plate and flow over backward facing step also show excellent agreement with the results reported in the literature.