Transport fidelity and domain of validity of compact Gaussian kinetic representations for rarefied flows

Abstract

Compact representations of rarefied flows must retain nonequilibrium transport information while identifying their range of validity. We investigate a common localized-Gaussian strategy for discrete-velocity-method (DVM) states in monatomic normal shocks and lid-driven cavities. The strategy is specialized to the available kinetic state: a positive phase-space mixture represents shock distributions and regenerates their moment hierarchy by quadrature, whereas a shared-support physical-space map represents 20 cavity fields. Localized support, continuous evaluation, transport fidelity, and coefficient-count accounting therefore provide the common structure across the two benchmarks. For separately fitted Mach-3 and Mach-5 shocks, the method gives sub-percent errors in conserved quantities and approximately 1--2\% errors in transport and higher-order moments. At the same 4608-coefficient budget, the tested multilinear grids produce 89--98\% errors in these nonequilibrium quantities. For both cavity cases, the Gaussian map also outperforms matched bilinear and singular-value-decomposition baselines, reducing maximum errors by factors of approximately 7--24. In the Mach-conditioned tests, a correspondence-preserving local basis reduces the withheld Mach-6 distribution error from $42.86\pm5.40\%$ to $11.45\pm0.94\%$ at fixed storage, while its transport errors remain 30--40\%; a normalized-coordinate guard rejects Mach 12 outside the training range. Independent grid studies confirm that these trends are not dominated by DVM discretization error. The results establish localized Gaussian representations as storage-efficient transport-fidelity maps for fitted kinetic states and provide quantitative acceptance criteria for parametric use.