A flux reconstruction solver for unsteady incompressible viscous flow using artificial compressibility with implicit dual time stepping

Abstract

This paper reports development of a high-order flux reconstruction method for solving unsteady incompressible flow on unstructured grids with implicit dual time stepping. The governing equations employ Chorin’s classic artificial compressibility treatment with dual time stepping. Implicit non-linear lower-upper symmetric Gauss-Seidel smoothing with backward Euler discretization is used to march the solution in pseudo time, while a second-order backward Euler discretization is used to march in physical time. We verify implementation of the high-order method coupled with our implicit time stepping scheme using incompressible Taylor-Green decaying vortices. We further validate the solver with unsteady laminar flow past a cylinder. The current implicit time stepping scheme is proven effective in satisfying the divergence-free constraint on the velocity field in the artificial compressibility formulation within the context of the high-order flux reconstruction method.