SFB 1313 Publication "Homogenization of Nonlocal Navier-Stokes-Korteweg Equations for Compressible Liquid-Vapor Flow in Porous Media"

December 7, 2020 /

Authors: Christian Rohde and Lars von Wolff
Scientific Journal: SIAM - Journal on Mathematical Analysis

New SFB 1313 publication, published in SIAM - Journal on Mathematical Analysis:

"Homogenization of Nonlocal Navier--Stokes--Korteweg Equations for Compressible Liquid-Vapor Flow in Porous Media"

Authors
Abstract

We consider a nonlocal version of the quasi-static Navier--Stokes--Korteweg equations with a nonmonotone pressure law. This system governs the low-Reynolds number dynamics of a compressible viscous fluid that may take either a liquid or a vapor 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 us 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.

We consider a nonlocal version of the quasi-static Navier--Stokes--Korteweg equations with a nonmonotone pressure law. This system governs the low-Reynolds number dynamics of a compressible viscous fluid that may take either a liquid or a vapor 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 us 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.


Read More: https://epubs.siam.org/doi/10.1137/19M1242434
We consider a nonlocal version of the quasi-static Navier--Stokes--Korteweg equations with a nonmonotone pressure law. This system governs the low-Reynolds number dynamics of a compressible viscous fluid that may take either a liquid or a vapor 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 us 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.


Read More: https://epubs.siam.org/doi/10.1137/19M1242434
We consider a nonlocal version of the quasi-static Navier--Stokes--Korteweg equations with a nonmonotone pressure law. This system governs the low-Reynolds number dynamics of a compressible viscous fluid that may take either a liquid or a vapor 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 us 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.


Read More: https://epubs.siam.org/doi/10.1137/19M1242434

SFB 1313 Publication "Homogenization of Nonlocal Navier-Stokes-Korteweg Equations for Compressible Liquid-Vapor Flow in Porous Media"

This image shows Christian Rohde

Christian Rohde

Prof. Dr. rer. nat.

Deputy Spokesperson, Principal Investigator, Research Projects B03 and C02, Project MGK

This image shows Lars von Wolff

Lars von Wolff

Dr.

Alumnus: Post-doctoral Researcher, Research Project C02

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