Development of a high-order implicit Discontinuous Galerkin method on unstructured meshes for turbomachinery flow - Min, Y (2018)
There is a continued need to further capabilities of turbomachinery flow design and analysis method tools, both in terms of the flow modeling fidelity (e.g. moving towards DES/LES) and temporal and spatial accuracy of the numerical discretization methods. To enhance solution accuracy with high-order methods, an implicit solver using the Discontinuous Galerkin (DG) discretization on unstructured meshes has been developed. The DG scheme is favored chiefly due to its distinctive feature that a higher-order accuracy being achieved through simple internal sub-divisions of a given mesh cell. It thus can considerably relieve the burden of mesh generation for local refinement of complex configurations. The implicit formulation is well suited for an unstructured mesh solver, for which some well-established solution techniques for explicit methods (e.g. multigrid methods) are less effective. The RANS equations in conjunction with the Sparlart-Allmaras one equation turbulence model are discretized using a high-order DG method on unstructured meshes. The all-speed AUSM+-up scheme is applied for the inviscid flux calculations and the BR2 scheme is implemented for the viscous flux discretization. An implicit time integration is adopted and the system linear equations are solved at each time step by using a preconditioned GMRES iterative algorithm with the ILU0. A modification of the turbulence model is also adopted to enhance the robustness for high-order turbulent flow simulations.