Hypersonic Nonequilibrium Flow Simulations Using a Robust and Efficient Temperature-Based Formulation

The simulation of thermochemical nonequilibrium hypersonic flows is critical for accurately predicting aerodynamic heating, pressure distribution, and shock interactions experienced by space vehicles during high-speed atmospheric flight and reentry. Traditional computational fluid dynamics (CFD) solvers for these environments often rely on a conservative variable-based formulation for nonequilibrium multi-temperature models. However, this formulation directly handles energy variables and thus requires iterative methods to extract temperatures essential for calculating various physical properties, resulting in increased computational costs and numerical instabilities, particularly in low-temperature regions. To overcome these challenges, we propose a novel temperature-based formulation that directly employs temperature variables instead of energy variables, eliminating the need for iterative temperature derivations. Additionally, we incorporate a low-temperature preconditioner combined with a solution-update limiter to enhance stability, particularly under low-temperature free-stream conditions. The low-temperature preconditioner modifies the Jacobian matrix to enhance diagonal dominance, effectively reducing numerical instabilities at extremely low temperatures. In addition, the solution-update limiter regulates the step size of temperature updates to prevent excessive changes, thereby decreasing the eigenvalue ratio and accelerating convergence. We also develop efficient chemical reaction models based on the least squares regression method. These regression-based models reformulate the original cumbersome process into a matrix-vector form, significantly reducing computational overhead. The proposed methods are integrated into our in-house finite volume solver, HyPer, which is specifically designed to handle arbitrary hyperbolic-type partial differential equations. The proposed methods are extensively validated through various hypersonic flow simulations on benchmark problems, demonstrating significant improvements in efficiency, robustness, and accuracy compared to the traditional approaches. These advancements highlight the potential of our framework for addressing the challenges of simulating thermochemical nonequilibrium hypersonic flows.