Multiscale thermodynamic nonequilibrium effects in Kelvin-Helmholtz instability and their relative importance

TL;DR

This paper explores the multiscale thermodynamic nonequilibrium effects during Kelvin-Helmholtz instability using high-order discrete Boltzmann models, providing new criteria and phase diagrams to understand and simulate different nonequilibrium regimes.

Contribution

It introduces a comprehensive analysis of TNE effects in KHI, proposes guidelines for discrete velocity set construction, and develops a nonequilibrium phase diagram to map multiscale nonequilibrium characteristics.

Findings

Identification of three TNE regimes during KHI development.

Criteria for TNE dominance based on relative thermodynamic nonequilibrium intensity.

Comparison of low- and high-order models revealing limitations of simpler models.

Abstract

This study investigates the complex kinetics of thermodynamic nonequilibrium effects (TNEs) and their relative importance during the development of Kelvin-Helmholtz instability (KHI) using high-order discrete Boltzmann models (DBMs). First, the capabilities and differences among various discrete velocity sets in capturing TNEs and distribution functions are assessed. Practical guidelines for constructing discrete velocity stencils are proposed to enhance phase-space discretization and improve the robustness of high-order DBM simulation. At different stages of KHI and under varying initial conditions, multiscale TNEs, such as viscous stresses of different orders, emerge with distinct dominant roles. Specifically, three scenarios are identified: (i) regimes dominated by first-order TNEs,(ii) alternation between first- and second-order TNEs, and (iii) states where second-order TNEs govern the system's behavior. To quantitatively capture these transitions, criteria for TNE dominance at different orders in KHI evolution are established based on the relative thermodynamic nonequilibrium intensity (\(R_{\text{TNE}}\)). In scenarios dominated by second-order TNEs, differences between first-order and second-order models are compared in terms of macroscopic quantities, nonequilibrium effects, and kinetic moments, revealing the physical limitations of low-order models in capturing TNEs. Furthermore, the effectiveness, extensibility, and limitations of a representative high-order model are examined under second-order TNE-dominated conditions. To encapsulate these findings, a nonequilibrium phase diagram that visually maps the multiscale characteristics of KHI is constructed. This diagram not only provides intuitive insights into the dynamic interplay of different nonequilibrium effects but also serves as a kinetic roadmap for selecting suitable models under diverse nonequilibrium conditions.