一维非混相两相流模型稳态解的分析与模拟
Analysis and Simulation of Steady-State Solutions for a One-Dimensional Immiscible Two-Phase Flow Model
摘要: 本文研究了一类非混相两相流模型，即一维可压缩Navier-Stokes/Allen-Cahn系统的稳态解及其界面极限问题。针对该模型的边值问题，证明了稳态解的存在性，并通过匹配渐近展开方法推导出界面层内的相场的近似解，结合经典BVP解算器和PINN方法，建立了精确的边界值问题求解框架，验证了该稳态解的界面极限。
Abstract: This paper investigates a class of immiscible two-phase flow models, namely the steady-state solutions and the interface limit of a one-dimensional compressible Navier-Stokes/Allen-Cahn system. For the associated boundary value problem, the existence of steady-state solutions is established. By means of matched asymptotic expansions, an approximate solution for the phase-field variable within the interfacial layer is derived. Furthermore, by combining classical boundary value problem solvers with physics-informed neural networks (PINNs), an accurate computational framework for solving the boundary value problem is developed, and the interface limit of the steady-state solution is numerically validated.
文章引用：桑梓桐, 陈亚洲. 一维非混相两相流模型稳态解的分析与模拟[J]. 应用数学进展, 2026, 15(2): 149-164. https://doi.org/10.12677/aam.2026.152057

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