Extension of the High-Order Entropy-stable Discontinuous Galerkin Solver to Non-Equilibrium Flows

Hypersonic flows encountered during atmospheric re-entry and high-speed aerospace operations demand robust CFD techniques. Under these extreme conditions, chemical non-equilibrium (CNEQ) and thermochemical non-equilibrium (TCNEQ) effects arise due to dissociation, ionization, and vibrational-electronic energy exchanges among multiple species and energy modes. Traditional CFD solvers that assume equilibrium conditions cannot accurately capture these complex physical phenomena.

The entropy-stable Discontinuous Galerkin (DG) solver developed at KAUST (SSDC) has demonstrated excellent accuracy and stability for single-species flow simulations. However, to extend its applicability to non-equilibrium hypersonic regimes, we must incorporate multi-species and multi-temperature modeling capabilities that account for high-temperature chemical reactions and inter-modal energy transfer.