Evaluation of a high-order central-difference solver for highly compressible flows out of thermochemical equilibrium

A high-order shock-capturing central finite-difference scheme is evaluated for numerical simulations of hyper-sonic high-enthalpy flows out of thermochemical equilibrium. The scheme is an extension to thermochemical out-of-equilibrium flows of the technique presented in Sciacovelli et al. (2021) for high-speed flows in chemical nonequilibrium. It relies on a standard tenth-order accurate central-difference approximation of the inviscid fluxes, supplemented with a high-order accurate nonlinear artificial dissipation term of ninth-order accuracy in smooth flow regions. Close to flow discontinuities, a shock-capturing low-order term is activated based on a highly selective shock sensor. To enable robust and non oscillatory solutions in regions of strong discontinuities of the thermodynamic variables, including the vibrational temperature, a shock detector consisting of a combination of a pressure-based term and Ducros' vorticity/dilatation sensor is applied to all conservation equations except that of vibrational energy. For the latter, a shock sensor based on the vibrational temperature itself is adopted instead, to account for the loose coupling between vibrational energy and pressure. The accuracy and robustness of the proposed approach is demonstrated for a variety of thermochemical non-equilibrium configurations, ranging from one-dimensional benchmarks to three-dimensional turbulent flows, for which the ILES capabilities of the selective high-order numerical dissipation are also showcased.