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Related papers: Thermodynamically Consistent Navier--Stokes--Cahn-…

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A Cahn-Hilliard-Navier-Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn-Hilliard energy with a singular (logarithmic) potential short time…

Analysis of PDEs · Mathematics 2025-11-18 Helmut Abels , Harald Garcke , Andrea Poiatti

A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and…

Analysis of PDEs · Mathematics 2011-02-22 Pierluigi Colli , Sergio Frigeri , Maurizio Grasselli

This work presents a macroscopic model for the flow of two immiscible and incompressible fluids within inhomogeneous porous media. At the pore scale, the flow is governed by the full Navier-Stokes equations while the phase interface…

Fluid Dynamics · Physics 2026-03-02 Chunhua Zhang , Peiyao Liu , Cheng Peng , Lian-Ping Wang , Zhaoli Guo

The motion of two contiguous incompressible and viscous fluids is described within the diffuse interface theory by the so-called Model H. The system consists of the Navier-Stokes equations, which are coupled with the Cahn-Hilliard equation…

Analysis of PDEs · Mathematics 2024-12-10 Andrea Giorgini , Alain Miranville , Roger Temam

Accurately modeling the dynamics of high-density ratio ($\mathcal{O}(10^5)$) two-phase flows is important for many material science and manufacturing applications. This work considers numerical simulations of molten metal oscillations in…

Fluid Dynamics · Physics 2025-01-03 Ali Rabeh , Makrand A. Khanwale , John J. Lee , Baskar Ganapathysubramanian

In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…

Analysis of PDEs · Mathematics 2025-03-06 Yinghua Li , Wenlin Ye

A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme.…

Computational Physics · Physics 2018-05-25 Xiaoyu Feng , Jisheng Kou , Shuyu Sun

We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…

Analysis of PDEs · Mathematics 2026-01-13 Bohan Ouyang , Maurizio Grasselli , Hao Wu

We show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier-Stokes/Cahn-Hilliard system with a solenoidal…

Analysis of PDEs · Mathematics 2020-10-14 Helmut Abels , Josef Weber

A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard…

Analysis of PDEs · Mathematics 2013-01-14 Sergio Frigeri , Maurizio Grasselli , Pavel Krejčí

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain by allowing for a degenerate mobility. The model has been developed by Abels, Garcke and…

Analysis of PDEs · Mathematics 2015-06-11 Helmut Abels , Daniel Depner , Harald Garcke

A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…

Analysis of PDEs · Mathematics 2020-07-28 Zhilei Liang , Dehua Wang

In this paper, we investigate the wellposedness of the non-isentropic compressible Navier-Stokes/Allen-Cahn system with the heat-conductivity proportional to a positive power of the temperature. This system describes the flow of a two-phase…

Analysis of PDEs · Mathematics 2020-11-13 Yazhou Chen , Qiaolin He , Bin Huang , Xiaoding Shi

We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we extend the block iterative method presented in Khanwale et…

Cahn-Hilliard-Navier-Stokes system describes the evolution of two isothermal, incompressible, immiscible fluids in a bounded domain. In this work, we consider the stationary nonlocal Cahn-Hilliard-Navier-Stokes system in two and three…

Analysis of PDEs · Mathematics 2020-10-01 Tania Biswas , Sheetal Dharmatti , P L N Mahendranath , Manil T Mohan

Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system…

Analysis of PDEs · Mathematics 2017-10-10 Helmut Abels , Harald Garcke , Josef Weber

The evolution of two partially miscible, nonhomogeneous, incompressible viscous fluids of non-Newtonian type, can be governed by the Navier-Stokes-Cahn-Hilliard system. In the present work, we prove the global existence of weak solutions…

Analysis of PDEs · Mathematics 2025-12-25 Fang Li , Duan Xingyu , Guo Zhenhua

We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier-Stokes equations for the volume averaged…

Analysis of PDEs · Mathematics 2024-04-17 Cecilia Cavaterra , Maurizio Grasselli , Muhammed Ali Mehmood , Riccardo Voso

The stationary Navier--Stokes--Cahn--Hilliard equations are considered, governing the motion of a compressible, two-phase fluid mixture with a diffuse interface. The free energy density in this paper has a singular logarithmic…

Analysis of PDEs · Mathematics 2026-05-05 Zhilei Liang , Sen Liu , Jiangyu Shuai , Dehua Wang