An arbitrary Lagrangian–Eulerian discontinuous Galerkin method for simulations of flows over variable geometries

A numerical method for simulations of flow over variable geometries including deformable domains or moving boundaries is presented in the context of high-order discontinuous Galerkin (DG) methods in the framework of an arbitrary Lagrangian Eulerian (ALE) description to take into account the deformable domains where boundaries are moving with prescribed motions or deformed under external forces. The ALE DG approach is shown to satisfy the geometric conservation law while preserving high-order accuracy. For variable geometries, we develop a simple and effective mesh smoothing technique based on element size functions to handle deformable grids due to moving boundaries. The current approach is applied to simulations of moving domain problems including laminar flows over oscillating cylinders and a flapping foil to show the ability of handling variable geometries with large deformation and high accuracy. The simulation results are compared with earlier experimental and numerical studies.