Homogenization of Non-Local Navier-Stokes-Korteweg Equations for Compressible Liquid-Vapour Flow in Porous Media

2019/02/19 by Rohde, Christian, von Wolff, Lars · 1 citation
#76M50 #76N99 #76T10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.07100

Abstract

We consider a nonlocal version of the quasi-static Navier-Stokes-Korteweg equations with a non-monotone pressure law. This system governs the low-Reynolds number dynamics of a compressible viscous fluid that may take either a liquid or a vapour state. For a porous domain that is perforated by cavities with diameter proportional to their mutual distance the homogenization limit is analyzed. We extend the results for compressible one-phase flow with polytropic pressure laws and prove that the effective motion is governed by a nonlocal version of the Cahn-Hilliard equation. Crucial for the analysis is the convolution-like structure of the nonlocal capillarity term that allows to equip the system with a generalized convex free energy. Moreover, the capillarity term accounts not only for the energetic interaction within the fluid but also for the interaction with a solid wall boundary.

Cited by

• Effective Equations for a Compressible Liquid-Vapor Flow Model with Highly Oscillating Initial Density

Related

• Convergence of capillary fluid models: from the non-local to the local Korteweg model
• On a Lagrangian method for the convergence from a non-local to a local Korteweg capillary fluid model
• Local in time results for local and non-local capillary Navier-Stokes systems with large data
• From nonlocal Euler-Korteweg to local Cahn-Hilliard via the high-friction limit
• Local well-posedness and asymptotic analysis of a nonlocal incompressible Navier--Stokes--Korteweg system