Beyond Fixed Thresholds: Situation-Aware Switching from Continuum to Kinetic Methods in Rarefied Gas Dynamics Simulations

Gas dynamics simulations which involve continuum-to-rarefied-to-ballistic flow transitions require physical models and numerical schemes of varying complexity depending on the local flow regime. In particular, accurate treatment of transitional and rarefied flows necessitates higher-fidelity kinetic solvers, while continuum regimes can be efficiently handled using lower-order continuum models. To span this spectrum, we use Gas-Kinetic Scheme (GKS) and Unified Gas-Kinetic Scheme (UGKS) as proxies for continuum and kinetic solvers, respectively. Hybrid frameworks that bridge these regimes typically employ switching parameters—such as Bird’s parameter (P), the local Knudsen number (Kn_GLL), or deviations from a local Maxwellian distribution—to detect non-equilibrium regions. These indicators are generally applied with fixed threshold criteria, each based on an implicit, fixed level of acceptable error. However, these static thresholds can lead to either significant flux errors or excessive, unnecessary use of high-fidelity solvers. This study proposes a user-driven, flow-aware switching framework in which the criterion parameter and the acceptable error tolerance (𝜀) are explicitly specified by the user, rather than fixed a priori. For each switching parameter, we calibrate the critical values as functions of the global Mach number (Ma_∞), Knudsen number (Kn_∞), and the user-defined 𝜀. This approach provides a generalizable and situation-aware switching mechanism, allowing different indicators to be used interchangeably and tuned to the desired accuracy. Importantly, the optimal switching criterion can be flow-dependent, reflecting the specific physical characteristics of the flow under study. We develop and demonstrate this robust framework in the context of shock flows, showing that it enables autonomous, accurate transitions between continuum and kinetic solvers without requiring real-time, in-situ comparisons.