Reductions of the Navier-Stokes-Allen-Cahn and the\n Navier-Stokes-Cahn-Hilliard equations

2013/11/01 by Heinrich Freistühler, Freistuhler, Heinrich, Matthias Kotschote +1
Computer Science · Engineering · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Navier-Stokes equation solutions #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1311.0125

openalex publication_date 2013/11/01 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

This paper studies two well-known models for two-phase fluid flow at constant\ntemperature, the isothermal Navier-Stokes-Allen-Cahn and the isothermal\nNavier-Stokes-Cahn-Hilliard equations, both of which consist of equations for\nthe (total) fluid density rho, the (mass-averaged)velocity u and the\nconcentration (of one of the phases,) c. Assuming in either case that both\nphases are incompressible with different densities, each of the models is shown\nto reduce to a system of evolution equations in rho and u alone. In the case of\nthe Navier-Stokes-Allen-Cahn model, this reduced system is the classical\nNavier-Stokes-Korteweg model. The reduced system resulting from the\nNavier-Stokes-Cahn-Hilliard equations is a novel `integro'-differential system\nin which a non-local operator acts on the divergence of the velocity.\n

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