A high-order flux reconstruction/correction procedure via reconstruction formulation for unsteady incompressible flow on unstructured moving grids. (5th November 2016) - Yu, Meilin; Wang, Lai
Highlights: A high-order FR/CPR method is developed for incompressible flow on moving grids. Geometric conservation law is implicitly enforced for moving grid simulation. LUSGS is used to accelerate dual time stepping for unsteady flow simulation. Convergence properties of the incompressible flow solver are verified. Several vortex-dominated flows over moving curved boundaries are simulated. Abstract: 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.