A kinetic BGK edge-based scheme including vibrational and electronic energy modes for high-Mach flows

A first principles formulation for the calorically imperfect behavior of gases is here proposed within a Boltzmann-type discretisation of the Navier–Stokes equations. The formulation is intended to enhance the consistency of gas kinetic schemes (GKS) with the physics of supersonic and hypersonic regimes where vibrational and electronic energy modes are activated before any thermal nonequilibrium or chemical activity takes place. The so-called node-pair BGK scheme, an edge-based implementation of the GKS, is considered in the present work for the implementation of a thermodynamic model where the calorically imperfect behavior is obtained from a modification of the way the different moments of the particle distribution function are computed and eventually used to determine the fluxes of conserved quantities across the boundary of each control volume. The method is validated on a series of canonical test cases for supersonic and hypersonic flows