Entropy-Aware Strategies in DG-Based Implicit Large Eddy Simulation for Turbulent Compressible Flows
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The embedding of structure-preserving properties onto high order schemes demonstrably improves the underlying robustness of the resolution algorithm. In this work, we enforce entropy consistent behaviour on a DG framework by coupling an L2 projection onto the entropy space with a local entropy correction. Since the projection operation is restricted to the spatial discrete operator, the resulting scheme maintains a computational complexity similar to the baseline conservative scheme, with the non-stationary term retained in its conservative form and time-integrated via a fourth order SSP-RK scheme. We show that the derived numerical framework proves to be an efficient and robust tool for undertaking under-resolved ILES simulation for challenging transonic/supersonic flows. As benchmark cases, we considered the M={1.5,3} channel flows at Ret up to 1000, and a M={0.95,1.2} flow impinging a sphere at Re=1000. The entropy-projected framework emerges as significantly more robust with respect to the baseline conservative scheme, enabling to accurately tackle the demanding conditions of the above mentioned simulations.
