TY - JOUR
T1 - A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities
AU - Ten Eikelder, M. F.P.
AU - Van Der Zee, K. G.
AU - Akkerman, I.
AU - Schillinger, D.
PY - 2023
Y1 - 2023
N2 - Over the last decades, many diffuse-interface Navier-Stokes Cahn-Hilliard (NSCH) models with non-matching densities have appeared in the literature. These models claim to describe the same physical phenomena, yet they are distinct from one another. The overarching objective of this work is to bring all of these models together by laying down a unified framework of NSCH models with non-zero mass fluxes. Our development is based on three unifying principles: (1) there is only one system of balance laws based on continuum mixture theory that describes the physical model, (2) there is only one natural energy-dissipation law that leads to quasi-incompressible NSCH models, (3) variations between the models only appear in the constitutive choices. The framework presented in this work now completes the fundamental exploration of alternate non-matching density NSCH models that utilize a single momentum equation for the mixture velocity, but leaves open room for further sophistication in the energy functional and constitutive dependence.
AB - Over the last decades, many diffuse-interface Navier-Stokes Cahn-Hilliard (NSCH) models with non-matching densities have appeared in the literature. These models claim to describe the same physical phenomena, yet they are distinct from one another. The overarching objective of this work is to bring all of these models together by laying down a unified framework of NSCH models with non-zero mass fluxes. Our development is based on three unifying principles: (1) there is only one system of balance laws based on continuum mixture theory that describes the physical model, (2) there is only one natural energy-dissipation law that leads to quasi-incompressible NSCH models, (3) variations between the models only appear in the constitutive choices. The framework presented in this work now completes the fundamental exploration of alternate non-matching density NSCH models that utilize a single momentum equation for the mixture velocity, but leaves open room for further sophistication in the energy functional and constitutive dependence.
KW - incompressible two-phase flow
KW - mixture theory
KW - Navier-Stokes Cahn-Hilliard equations
KW - phase-field models
KW - thermodynamic consistency
UR - http://www.scopus.com/inward/record.url?scp=85149237824&partnerID=8YFLogxK
U2 - 10.1142/S0218202523500069
DO - 10.1142/S0218202523500069
M3 - Article
AN - SCOPUS:85149237824
SN - 0218-2025
VL - 33
SP - 175
EP - 221
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 1
ER -