From kinetic mixtures to compressible two-phase flow: A BGK-type model and rigorous derivation
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911020369313792 |
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| author | Cho, Seung Yeon Choi, Young-Pil Hwang, Byung-Hoon Song, Sihyun |
| author_facet | Cho, Seung Yeon Choi, Young-Pil Hwang, Byung-Hoon Song, Sihyun |
| contents | We propose a BGK-type kinetic model for a binary gas mixture, designed to serve as a kinetic formulation of compressible two-phase fluid dynamics. The model features species-dependent adiabatic exponents, and the relaxation operator is constructed by solving an entropy minimization problem under moments constraints. Starting from this model, we derive the compressible two-phase Euler equations via a formal Chapman--Enskog expansion and identify dissipative corrections of Navier--Stokes type. We then rigorously justify the Euler limit using the relative entropy method, establishing quantitative convergence estimates under appropriate regularity assumptions. Finally, we present numerical experiments based on an implicit-explicit Runge--Kutta method, which confirm the asymptotic preserving property and demonstrate the convergence from the BGK model to the isentropic two-phase Euler system in the hydrodynamic regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From kinetic mixtures to compressible two-phase flow: A BGK-type model and rigorous derivation Cho, Seung Yeon Choi, Young-Pil Hwang, Byung-Hoon Song, Sihyun Analysis of PDEs Numerical Analysis We propose a BGK-type kinetic model for a binary gas mixture, designed to serve as a kinetic formulation of compressible two-phase fluid dynamics. The model features species-dependent adiabatic exponents, and the relaxation operator is constructed by solving an entropy minimization problem under moments constraints. Starting from this model, we derive the compressible two-phase Euler equations via a formal Chapman--Enskog expansion and identify dissipative corrections of Navier--Stokes type. We then rigorously justify the Euler limit using the relative entropy method, establishing quantitative convergence estimates under appropriate regularity assumptions. Finally, we present numerical experiments based on an implicit-explicit Runge--Kutta method, which confirm the asymptotic preserving property and demonstrate the convergence from the BGK model to the isentropic two-phase Euler system in the hydrodynamic regime. |
| title | From kinetic mixtures to compressible two-phase flow: A BGK-type model and rigorous derivation |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2506.19321 |