Development of a coupled matrix-free LU-SGS solver for hypersonic laminar diatomic gas flows with decoupled vibrational energy mode

This study presents a newly developed implicit solver for steady-state, thermally non-equilibrium, hypersonic laminar diatomic gas flows. The algorithm focuses on cases where the gas is highly vibrationally excited, necessitating the consideration of decoupled internal energy modes. This phenomenon is modeled using the Navier–Stokes equations, along with an additional transport equation for vibrational energy. Implemented within the OpenFOAM framework, the solver employs the finite volume method with an approximate HLLC Riemann solver, enhanced with a low-Mach correction. Furthermore, limited piecewise linear reconstructions are used for convective fluxes, while viscous fluxes are approximated using a central scheme. Time marching is performed using the first-order backward differentiation formula. The resulting equations are solved using a matrix-free lower-upper symmetric Gauss–Seidel scheme, enabling efficient simulations with a low memory footprint. The developed solver is applied to solve two distinct axisymmetric hypersonic flow problems: hollow-cylinder-flare and double-cone flows, both computed for two different sets of free-stream and wall conditions. The results are compared with experimental data and those obtained from equilibrium simulations. Finally, a comparison with a well-known explicit non-equilibrium solver and simulation data from literature is provided, focusing on accuracy and performance.