WENO-enhanced gas-kinetic scheme for direct simulations of compressible transition and turbulence

The recently developed Gas Kinetic Method (GKM) for computing fluid flow is enhanced with advanced reconstruction (interpolation) schemes to enable direct simulations of highly compressible transition and turbulence fields. Variants of Weighted Essentially Non-Oscillatory (WENO) reconstruction schemes of different orders of accuracy are implemented and examined along with more elementary van Leer method. The competing schemes are evaluated for their accuracy, efficiency and numerical stability. The computed results are compared against the Rapid Distortion Theory for the case of compressible shear turbulence and 'pressure-released' Burgers solution. In the case of decaying isotropic turbulence, the efficacy of the reconstruction schemes is evaluated by comparison against a 'gold standard' high-resolution simulation. The capabilities of the reconstruction schemes to capture linear, non-linear, pressure-released and viscous flow physics as well as solenoidal and dilatational features of the flow fields are established in isolation and combination. The most suitable WENO variant for integration with GKM is identified. Another important outcome of the study is the finding that temperature-interpolation is superior to energy-interpolation in avoiding negative temperatures arising due to the Gibbs phenomenon. Overall, this work advances the applicability of kinetic theory based GKM to a wider range of high Mach number flow physics.