Matrix-Free LU-SGS Solver for Hypersonic Laminar Diatomic Gas Flows with Decoupled Vibrational Energy Mode: Mesh Effects on Shock Waves and Separation Bubble in Double-Cone Flow

A matrix-free implicit finite-volume solver based on the LU-SGS method is applied to the simulation of hypersonic laminar diatomic gas flows with a decoupled vibrational energy mode. The solver is implemented within the OpenFOAM framework and solves the Navier-Stokes equations extended by a transport equation for vibrational energy to account for thermal non-equilibrium effects. The numerical method is assessed through a systematic mesh-dependency study of axisymmetric double-cone flows, a canonical configuration exhibiting strong shock-shock and shock-boundary-layer interactions accompanied by flow separation. Three successively refined structured meshes are used to examine the influence of spatial resolution on shock structure, wall-pressure distribution, and separation bubble characteristics. The results demonstrate a strong sensitivity of separation length and shock position to mesh refinement. Increased resolution leads to reduced peak wall pressure but a more extended adverse pressure gradient, resulting in longer predicted separation bubbles. These findings highlight the critical role of mesh resolution in hypersonic non-equilibrium simulations and underline the need for careful grid design when predicting shock-induced separation in laminar high-speed flows.