Implementation and testing of unsteady Reynolds-averaged Navier-Stokes and detached eddy simulation using an implicit unstructured multigrid scheme

Investigation and development of the Detached Eddy Simulation (DES) technique for the computation of unsteady flows on unstructured grids are presented. The motivation of the research work is driven by the ultimate goal of predicting separated flows of aerodynamic importance, such as massive stall or flows over complex non-streamlined geometries. These cases, in which large regions of massively separated flow are present, represent a challenge for conventional Unsteady Reynolds-Averaged Navier-Stokes (URANS) models, that in many cases, cannot produce solutions accurate enough and/or fast enough for industrial design and applications. A Detached Eddy Simulation model is implemented and its performance compared to the one equation Spalart-Allmaras Reynolds-Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and URANS include decaying homogenous turbulence in a periodic domain, flow over a sphere and flow over a wing with a NACA 0012 profile, including massive stall regimes.; Because of the inherent unsteadiness of turbulence, the first step towards computing separated flows is the development of an unsteady solution technique for unstructured meshes to be able to produce time accurate solutions. An implicit method for the computation of unsteady flows on unstructured grids was implemented based on an existing steady state multigrid unstructured mesh solver. The resulting non-linear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the time accurate URANS solver is performed for the well-known case of flow over a cylinder.