Robust and Efficient Implementation of Very High-Order Discontinuous Galerkin Methods in CFD

Discontinuous Galerkin (DG) methods are a very powerful numerical techniques, that offer high degree of robustness, accuracy and flexibility, nowadays necessary for the solution of complex fluid flows. The drawback is the relatively high computational cost and storage requirement. This work will focus on two ap- proaches which can be adopted to enhance the computational efficiency of this class of methods: (i) a DG discretization based upon co-located tensor product basis func- tions, and (ii) a p-multigrid solution strategy. The effectiveness of the proposed ap- proaches has been demonstrated by computing 3D inviscid and turbulent test cases.