Kinetic and macroscopic modelling for dense gas flow simulations

Abstract

This study delves into the complexities of modelling dense gases near thermodynamic critical points, where conventional gas dynamic assumptions prove inadequate. Within this unique regime, non-linear waves exhibit behaviours divergent from classical phenomena, like expansion shocks which remain consistent with entropy conditions. Accurately capturing these phenomena mandates sophisticated equation of state (EoS) that surpasses the ideal gas assumptions, presenting challenges for numerical simulations. In this paper, we propose a simple modification to the Boltzmann equation (with the BGK framework), which, upon taking moments, leads to Euler equations for dense gas flows. We consider van der Waals EoS. Further, we develop a three-velocity model based Kinetic Flux Difference Splitting (KFDS) scheme for the Euler system, with adaptable diffusion coefficients suitable to capture compressible flow phenomena specific to ideal and dense gases. This innovative approach diverges from traditional algorithms, which are tailored for ideal gas EoS and struggle to accommodate the inherent variations. A comparative analysis with macroscopic efficient central solvers designed to be independent of the eigen-structure, such as MOVERS+ and RICCA, is conducted to validate the results against benchmark tests from the data in the literature. It is important to note that the kinetic schemes also possess the advantage of being independent of the eigen-structure, a feature that distinguishes them from traditional Riemann solvers. This effort significantly enhances computational modelling capabilities and fosters deeper insights into the behaviour of dense gases. The proposed advancements enhance numerical methods tailored for real gas EoS simulations by ensuring precise capture of grid-aligned steady discontinuities and effectively mitigating numerical diffusion across these discontinuities in inviscid compressible flows.