A log-Gaussian scale-space limiter for hybrid continuum–ballistic gas dynamics

Abstract

Rarefied hypersonic gas flows involve a continuous competition between collisional relaxation and ballistic molecular transport. Classical Chapman–Enskog hydrodynamics is valid when the local Knudsen number is small, whereas free-molecular or kinetic descriptions are required when the molecular mean free path becomes comparable to or larger than the macroscopic variation length. Existing multiscale kinetic schemes provide robust treatments across these regimes but may be expensive when embedded in large-scale continuum solvers. In this work, we propose a log-Gaussian scale-space limiter for hybrid continuum–ballistic gas dynamics. The local Knudsen number is interpreted as a stochastic scale ratio, and the transition between collisional and ballistic transport is modeled as a probability partition in logarithmic Knudsen space. The resulting continuum and ballistic weights are complementary Gaussian cumulative probabilities. This construction provides super-algebraic suppression of inverse-Knudsen corrections in the continuum limit and of Chapman–Enskog corrections in the free-molecular limit. A conservative interface flux is then built by blending a Navier–Stokes–Fourier flux with a half-range Maxwellian kinetic flux. The proposed framework preserves the conservative structure of the macroscopic equations, recovers the continuum and free-molecular limits, and provides a physically interpretable transition mechanism for high-Mach rarefied flows. The method is formulated as a lightweight hybrid closure intended for future implementation in finite-volume, discrete Boltzmann, or gas-kinetic solvers. Reduced one-dimensional closure/profile comparisons against Discrete Velocity Method/Bhatnagar–Gross–Krook (DVM/BGK) Fourier and Couette data show that log-Gaussian weighting of Navier–Stokes–Fourier (NSF) and jump/slip-corrected branches improves the tested macroscopic profiles relative to NSF. The same six DVM/BGK profiles are used both as reference profiles and to calibrate K ₀ and σ ; therefore, the approximately 40 % reduction in combined mean profile error is an in-sample calibration result for the reduced profile model rather than independent validation or a numerical validation of the proposed finite-volume face flux. Additional diagnostics assess non-equilibrium moments, internal parameter robustness, and activation of the local rarefaction indicator in analytic shock-like profiles, reduced one-velocity DVM/BGK shock layers, and two-dimensional curved shock geometries.