A high-order flux reconstruction/correction procedure via reconstruction formulation for unsteady incompressible flow on unstructured moving grids

A high-order accurate flux reconstruction/correction procedure via reconstruction (FR/CPR) method is developed to solve unsteady incompressible Navier-Stokes equations on unstructured moving grids. An artificial compressibility method is adopted to facilitate the common flux reconstruction on element interfaces. A dual-time stepping method accelerated by the lower-upper symmetric-Gauss-Siedel scheme is used to solve unsteady flow problems. An arbitrary Lagrangian-Eulerian approach is adopted for simulations on moving/deforming grids. The geometric conservation law is implicitly incorporated into the governing equations which are discretized using the FR/CPR formulation. Convergence properties of the developed method are verified with the circular Couette flow over curved boundaries and a manufactured flow on moving meshes. The capability of the flow solver to capture vortex-dominated flows is then tested with unsteady flows over oscillating cylinders and airfoils. It is concluded that the developed FR/CPR flow solver can effectively simulate unsteady incompressible flows on moving grids.