Explicit time accurate pseudo-compressibility method for numerical solutions of unsteady incompressible viscous flows

An explicit time accurate pseudo compressibility method has been proposed for numerical solutions of unsteady incompressible viscous flows. It is based on the method of lines approach using an explicit time integration scheme for both physical and pseudo-time. The one-stage three-level Runge-Kutta scheme is applied for time integration in physical time and the rational Runge-Kutta scheme is applied for that in pseudo-time. The multigrid scheme, residual averaging, and local time stepping are incorporated in order to accelerate convergence to steady state in pseudo-time. In this paper, numerical solutions of the simple Poisson equation, one-dimensional oscillating channel flow and two -dimensional flow around a cylinder at Re=200 are presented. It is shown that the present scheme is reliable in accuracy and requires less computing cost than a conventional scheme using the SOR method.