English
Related papers

Related papers: On a diffuse interface model for incompressible vi…

200 papers

A modal stability analysis shows that pressure-driven pipe flow of an Oldroyd-B fluid is linearly unstable to axisymmetric perturbations, in stark contrast to its Newtonian counterpart which is linearly stable at all Reynolds numbers. The…

Fluid Dynamics · Physics 2020-12-09 Indresh Chaudhary , Piyush Garg , Ganesh Subramanian , Viswanathan Shankar

The steady flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens model for blood) in a two-dimensional channel, partly bound by a deformable, finite thickness neo-Hookean solid, is computed. The limiting Weissenberg number beyond…

Soft Condensed Matter · Physics 2020-07-03 Debadi Chakraborty , J. Ravi Prakash

When a viscous fluid partially fills a Hele--Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman--Taylor instability. We consider the evolution of a fluid region of finite extent, bounded…

Fluid Dynamics · Physics 2024-05-20 Michael C Dallaston , Michael J W Jackson , Liam C Morrow , Scott W McCue

The formal sharp-interface asymptotics in a degenerate Cahn-Hilliard model for viscoelastic phase separation with cross-diffusive coupling to a bulk stress variable are shown to lead to non-local lower-order counterparts of the classical…

Analysis of PDEs · Mathematics 2026-05-22 Katharina Hopf , John King , Andreas Münch , Barbara Wagner

In this paper, a phase-field based model under the framework of discrete unified gas-kinetic scheme (DUGKS) for incompressible multiphase fluid flows is proposed. Two kinetic models are constructed to solve the conservative Allen-Cahn (A-C)…

Computational Physics · Physics 2019-04-10 Zeren Yang , Chengwen Zhong , Congshan Zhuo

In this paper, we propose and analyze a diffuse interface model for inductionless magnetohydrodynamic fluids. The model couples a convective Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes system for fluid flow…

Analysis of PDEs · Mathematics 2023-12-20 Xiaodi Zhang

We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…

Analysis of PDEs · Mathematics 2020-07-22 Michal Bathory , Miroslav Bulíček , Josef Málek

We consider a simple nonlinear hyperbolic system modeling the flow of an inviscid fluid. The model includes as state variable the mass density fraction of the vapor in the fluid and then phase transitions can be taken into consideration;…

Analysis of PDEs · Mathematics 2014-08-27 Debora Amadori , Paolo Baiti , Andrea Corli , Edda Dal Santo

The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple…

Fluid Dynamics · Physics 2009-10-31 Mikhail V. Khenner , Dmitrii V. Lyubimov , Tatyana S. Belozerova , Bernard Roux

We propose a new Cahn-Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive…

Analysis of PDEs · Mathematics 2023-01-23 Abramo Agosti , Pierluigi Colli , Harald Garcke , Elisabetta Rocca

In this paper, we consider viscoelastic flows in a rough domain (with typical roughness patterns of size $\epsilon$ < 1). We present and rigorously justify an asymptotic expansion with respect to $\epsilon$, at any order, based upon the…

Analysis of PDEs · Mathematics 2015-03-12 Laurent Chupin , Sébastien Martin

We analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressible two-phase flows where the mechanisms of chemotaxis, active transport and reaction are taken into account. The evolution system couples the Navier-Stokes equations for…

Analysis of PDEs · Mathematics 2024-06-03 Jingning He , Hao Wu

An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is…

Analysis of PDEs · Mathematics 2025-06-13 S. N. Antontsev , H. B. de Oliveira , I. V. Kuznetsov , D. A. Prokudin , Kh. Khompysh

An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large…

Numerical Analysis · Mathematics 2013-03-20 Stefan Engblom , Minh Do-Quang , Gustav Amberg , Anna-Karin Tornberg

This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…

Computational Physics · Physics 2021-06-04 Tim Wallis , Philip T. Barton , Nikolaos Nikiforakis

This paper is concerned with a diffusion model of phase-field type, consisting of a parabolic system of two partial differential equations, interpreted as balances of microforces and microenergy, for two unknowns: the problem's order…

Analysis of PDEs · Mathematics 2011-09-16 Pierluigi Colli , Gianni Gilardi , Paolo Podio-Guidugli , Jürgen Sprekels

We consider a phase field model for the flow of two partly miscible incompressible, viscous fluids of Non-Newtonian (power law) type. In the model it is assumed that the densities of the fluids are equal. We prove existence of weak…

Analysis of PDEs · Mathematics 2013-02-14 Helmut Abels , Lars Diening , Yutaka Terasawa

In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier-Stokes equations in the two fluid phases, connected by…

Numerical Analysis · Mathematics 2026-02-11 Harald Garcke , Robert Nürnberg , Dennis Trautwein

The problem of oscillating flows inside pipes under periodic forcing of viscoelastic fluids is addressed here. Starting from the linear Oldroyd-B model, a generalized Darcy's law is obtained in frequency domain and an explicit expression…

In this paper, we propose an improved phase field model for interface capturing in simulating two-phase incompressible flows. The model incorporates a second-order diffusion term, which utilizes a nonlinear coefficient to assess the degree…

Fluid Dynamics · Physics 2025-01-20 Jing-Wei Chen , Chun-Yu Zhang , Hao-Ran Liu , Hang Ding