Discrete Boltzmann modeling of high-speed compressible flows with various depths of non-equilibrium

TL;DR

This paper develops Discrete Boltzmann Models considering various orders of Thermodynamic Non-Equilibrium effects to accurately simulate high-speed compressible flows with different non-equilibrium levels, validated through multiple flow problems.

Contribution

It introduces a flexible DBM framework that captures higher-order TNE effects, enhancing the modeling of complex high-speed flows beyond traditional approaches.

Findings

The model accurately captures large flow structures and fine molecular-scale details.

Higher-order TNE effects are necessary for precise hydrodynamic quantities.

Different TNE measures reveal varying degrees of non-equilibrium in flows.

Abstract

The non-equilibrium high-speed compressible flows present wealthy applications in engineering and science. With the deepening of Thermodynamic Non-Equilibrium (TNE), higher-order non-conserved kinetic moments of the distribution function are needed to capture the main feature of the flow state and evolution process. Based on the ellipsoidal statistical Bhatnagar-Gross-Krook model, Discrete Boltzmann Models (DBMs) that consider various orders (from the first up to the sixth order) of TNE effects are developed to study flows in various depths of TNE. Specifically, at first, two types of one-dimensional Riemann problems and a Couette flow are used to show the model's capability to capture large flow structures with zero-order and first-order TNE effects, respectively. Then, a shock wave structure given by Direct simulation Monte Carlo is used to verify the model's capability to capture fine structures at the level of mean free path of molecules. Further, we focus on the TNE degree of two colliding fluids. A five-component vector $\mathbf{S}_{TNE} = (\tau, \Delta \mathbf{u}, \Delta T, \bm{\Delta_{2}^{*}},\bm{\Delta_{3,1}^{*}})$ is introduced to roughly characterize the TNE degree. It is found that the TNE strengths obtained from various perspectives are different. These findings demonstrate that the inadequacy of focusing only on the few kinetic moments appearing in Navier-Stokes increases with the degree of discreteness and deviation from thermodynamic equilibrium. Finally, a two-dimensional free jet is simulated to indicate that, to obtain satisfying hydrodynamic quantities, the DBM should include at least up to the third-order TNE effects.