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Related papers: On a Thermodynamically Consistent Diffuse-Interfac…

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We consider an initial-boundary value problem for the chemotaxis-Navier--Stokes system \begin{align*} \left\{ \begin{array}{c@{\quad}l@{\quad}l@{\,}c} n_{t}+u\cdot\nabla n=\nabla\cdot\big(D(n)\nabla n-nS(x,n,c)\cdot\nabla c\big),\…

Analysis of PDEs · Mathematics 2025-06-18 Tobias Black

We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…

Numerical Analysis · Mathematics 2023-12-29 Gauthier Wissocq , Rémi Abgrall

We consider a computational model for complex-fluid-solid interaction based on a diffuse-interface model for the complex fluid and a hyperelastic-material model for the solid. The diffuse-interface complex-fluid model is described by the…

Numerical Analysis · Mathematics 2015-10-09 E. H. van Brummelen , M. Shokrpour-Roudbari , G. J. van Zwieten

A numerical study is presented to analyze the thermal mechanisms of unsteady, supersonic granular flow, by means of hydrodynamic simulations of the Navier-Stokes granular equations. For this purpose a paradigmatic problem in granular…

Fluid Dynamics · Physics 2015-06-04 Lidia Almazán , José A. Carrillo , Clara Salueña , Vicente Garzó , Thorsten Poeschel

Ferrofluids are a class of materials that exhibit both fluid and magnetic properties. We consider a two-phase diffuse interface model for the dynamics of ferrofluids on a bounded domain. One phase is assumed to be magnetic, the other phase…

Analysis of PDEs · Mathematics 2025-07-08 Samuel Lanthaler , Franziska Weber

The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the…

Numerical Analysis · Mathematics 2022-10-18 Ronald A. Remmerswaal , Arthur E. P. Veldman

In this article we consider two different heat conducting fluids each modelled by the incompressible Navier-Stokes-Fourier system separated by a non-linear elastic Koiter shell. The motion of the shell changes the domain of definition of…

Analysis of PDEs · Mathematics 2026-02-12 Sourav Mitra , Sebastian Schwarzacher

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…

Fluid Dynamics · Physics 2011-04-08 H. Abels , H. Garcke , G. Grün

We consider an initial-boundary value problem for the incompressible chemotaxis-Navier-Stokes equations generalizing the porous-medium-type diffusion model $ \quad n_t+u\cdot\nabla n=\Delta n^m-\nabla\cdot(n\chi(c)\nabla c), $ $ \quad…

Analysis of PDEs · Mathematics 2015-01-22 Qingshan Zhang , Yuxiang Li

In this paper we investigate the compressible Navier-Stokes-Cahn-Hilliard equations (the so-called NSCH model) derived by Lowengrub and Truskinowsky. This model describes the flow of a binary compressible mixture; the fluids are supposed to…

Analysis of PDEs · Mathematics 2013-06-12 Matthias Kotschote , Rico Zacher

This paper studies the dynamics of two incompressible immiscible fluids in 2D modeled by the inhomogeneous Navier-Stokes equations. We prove that if initially the viscosity contrast is small then there is global-in-time regularity. This…

Analysis of PDEs · Mathematics 2022-08-02 Francisco Gancedo , Eduardo Garcia-Juarez

We study the well-posedness of a coupled Cahn-Hilliard-Stokes-Darcy system which is a diffuse-interface model for essentially immiscible two phase incompressible flows with matched density in a karstic geometry. Existence of finite energy…

Analysis of PDEs · Mathematics 2014-05-22 Daozhi Han , Xiaoming Wang , Hao WU

Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics, these models are generally distinct, and an overarching…

Fluid Dynamics · Physics 2025-04-01 M. F. P. ten Eikelder

We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…

Analysis of PDEs · Mathematics 2018-03-20 Inwon Kim , Alpár R. Mészáros

Starting from a microscopic multiparticle Langevin equation, we systematically derive a hydrodynamic description in terms of density and momentum fields for chiral active particles interacting via standard repulsive and nonlocal odd forces.…

Soft Condensed Matter · Physics 2026-01-28 Umberto Marini Bettolo Marconi , Alessandro Petrini , Raphaël Maire , Lorenzo Caprini

We present a thermodynamically consistent phase-field model for simulating fluid transport across semi-permeable membranes, with a particular focus on osmotic pressure effects. The model extends the classical Navier-Stokes-Cahn-Hilliard…

Fluid Dynamics · Physics 2025-06-16 Ruihan Guo , Jie Shen , Shixin Xu , Xianmin Xu

In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in $3D$ domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the…

Analysis of PDEs · Mathematics 2017-10-10 Blanca Climent-Ezquerra , Francisco Guillén-González

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes…

Analysis of PDEs · Mathematics 2016-02-17 C. Grandmont , M. Hillairet

We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…

Analysis of PDEs · Mathematics 2022-01-19 Helmut Abels , Yutaka Terasawa

We propose a new diffuse interface model for simulating an inductionless magnetohydrodynamic (MHD) free surface problem. By using the Onsager's variational principle and the laws of thermodynamics, we derive a thermodynamically consistent…

Numerical Analysis · Mathematics 2025-09-29 Jiancheng Wang , Maojun Li , Zeyu Xia , Liwei Xu