An entropy-aware discontinuous Galerkin solver for implicit large eddy simulations of wall-bounded flows

A high-order modal discontinuous Galerkin framework, embedding an efficient strategy to ensure entropy conservation/stability at discrete level, is here exploited to perform highly challenging implicit large eddy simulations of turbulent channel flows. Together with more explored incompressible configurations, the numerical scheme is also tested for several highly compressible cases. Such simulations are undertaken in conditions of both moderate and extreme under-resolution, up to reaching discrete solutions that employ approximately 1/2000 of the degrees of freedom of the reference direct numerical simulation. We show that the numerical properties of the framework may be leveraged to impose a "correct" dissipation on the numerical solution in order to derive remarkably accurate results in condition of strong under-resolution. In the near-incompressible regime, optimal accuracy on poorly resolved space discretizations is obtained upon adoption of a low-dissipation entropy-conserving convective scheme, combined with suitably constructed wall boundary conditions. Conversely, for high-Mach number flows, the interplay of compressibility and under-resolution results in flow configurations that benefits from the implementation of a fully entropy-stable discretization of the convective terms. Overall, we are able to show that the entropy-aware framework is sufficiently robust to run challenging simulations with virtually no numerical dissipation, so that a fine-tuning of the latter may be suitably designed to achieve accurate results.