Unsteady Simulation of Incompressible Flows on Unstructured Grids Using the Implicit IRK-SIMPLER Algorithm

摘要

An implicit Runge-Kutta based algorithm for unsteady incompressible flows, IRK-SIMPLER, is developed on unstructured grids. IRK-SIMPLER is tested on a triangular grid using a vertex-centered median-dual control volume formulation, and simulation results are compared to the legacy SIMPLER algorithm and the explicit RK-SIMPLER algorithm on the same grid. IRK-SIMPLER is shown to result in accurate solutions in less runtime than SIMPLER or RK-SIMPLER by requiring between 3-5 less runtime per time step than SIMPLER while maintaining the stability of an implicit algorithm and improving accuracy. Also developed is a new flux interpolation scheme for unstructured grids called the Flux Corrected Method (FCM). FCM uses a small stencil and includes more of the known physics into the momentum flux interpolation such as pressure gradient and unsteady terms. FCM is able to improve the accuracy compared to the Power Law scheme without increasing the number of nodes or elements, i.e. FCM is more accurate then Power Law and takes approximately the same runtime.