Formal derivation of an isentropic two-phase flow model from the multi-species Boltzmann equation

2025/06/16 by Gabriella Puppo, Puppo, Gabriella, Thomas Rey +3 · 1 citation
Mathematics · Engineering · #Gas Dynamics and Kinetic Theory #Particle Dynamics in Fluid Flows #Granular flow and fluidized beds

paper · doi:10.48550/arxiv.2506.13480

Abstract

Starting from the multispecies Boltzmann equation for a gas mixture, we propose the formal derivation of the isentropic two-phase flow model introduced in E. Romenski, D. Drikakis, and E. Toro [J. Sci. Comput. 42, 68 (2010)10.1007/s10915-009-9316-y]. We examine the asymptotic limit as the Knudsen numbers approach zero, in a regime characterized by resonant intraspecies collisions, where interactions between particles of the same species dominate. This specific regime leads to a multivelocity and multipressure hydrodynamic model, enabling the explicit computation of the coefficients for the two-phase macroscopic model. Our derivation also accounts for the inclusion of the evolution of the volume fraction, which is a key variable in many macroscopic multiphase models.

Citations

• A space-dependent Boltzmann-BGK model for gas mixtures and its hydrodynamic limits
• The Boltzmann equation for a multi-species inelastic mixture
• Explicit spectral gap estimates for the linearized Boltzmann operator modeling reactive gaseous mixtures
• The Cauchy problem for Boltzmann bi-linear systems: The mixing of monatomic and polyatomic gases
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• Rigorous derivation of the Fick cross-diffusion system from the\n multi-species Boltzmann equation in the diffusive scaling
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