Development of unsteady algorithms for pressure-based unstructured solver for two-dimensional incompressible flows

Development of unsteady algorithms for incompressible flow on triangular unstructured grids is presented. The numerical method used is derived from the SIMPLER algorithm. The spatial discretization is vertex-centered with median-dual control volume. The equal order velocity pressure interpolation method is employed to avoid the checkerboard pressure oscillation commonly encountered in using a collocated grid for solving incompressible flows. The time integration methods implemented are Fully-Implicit, Crank-Nicolson and a new explicit four-step Runge-Kutta method for incompressible flows. The Fully-Implicit and Crank-Nicolson follow the traditional path of a pressure correction equation to update the velocities. The Runge-Kutta SIMPLER uses the four-stage Runge-Kutta to update the velocities directly without a pressure correction equation. The resulting algorithms have been validated using the standard lid driven cavity problem and the backward facing step channel. The schemes are capable of capturing the unsteady or transient behavior in vortex development such as observed in the step channel flow. The unsteady algorithms have also been applied to the unsteady flow over a vertical flat plate. Simulation results and observations regarding the behavior of the different algorithms are presented.