Efficient Compressible Turbulent Flow Simulations: Entropy Projection and Correction for an ILES in a Discontinuous Galerkin solver

We present the assessment of an entropy projection-correction approach, embedded on a high order discontinuous Galerkin (DG) scheme, as an effective and efficient solution for undertaking under-resolved implicit Large Eddy simulations (iLES) of turbulent transonic/ supersonic flows. Combining the L2 projection of the discrete spatial operators onto the entropy variable space with the residual correction of [1] we achieve an entropy conserving/stable (EC/ES) DG discretization of the convective operators upon suitable choice of the associated numerical flux function. The resulting framework shows an improved robustness which is exploited to tackle iLES on severely under-resolved space discretizations, achieving remarkably accurate solutions even on such coarse computational spaces.