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We present and analyze a variational front-tracking method for a sharp-interface model of multiphase flow. The fluid interfaces between different phases are represented by curve networks in two space dimensions (2d) or surface clusters in…

Numerical Analysis · Mathematics 2026-02-11 Harald Garcke , Robert Nürnberg , Quan Zhao

It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…

Fluid Dynamics · Physics 2014-08-04 Maxim Zaytsev , Vyacheslav Akkerman

The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interface through the continuity of the velocity and traction…

Analysis of PDEs · Mathematics 2009-11-11 Daniel Coutand , Steve Shkoller

The Navier-Stokes-Voigt (NSV) model of viscoelastic incompressible fluid has been recently proposed as a regularization of the 3D Navier-Stokes equations for the purpose of direct numerical simulations. In this work we investigate its…

Fluid Dynamics · Physics 2009-01-06 Boris Levant , Fábio Ramos , Edriss S. Titi

In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the…

Numerical Analysis · Mathematics 2011-05-09 Bernard Di Martino , Catherine Giacomoni , Jean-Martin Paoli , Pierre Simonnet

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

The viscous interaction of fluid is understood as the response to deformation, which is proportional to the strain rate. This model has gradually become the standard since Stokes, and has become the basis of the classical flow theory,…

Fluid Dynamics · Physics 2023-06-27 Jian He , Jin Wang , Qiaocong Kong , Penglong Zhao , Xiaoshu Cai , Xiaohang Zhang , Wennan Zou

Viscous contact problems describe the time evolution of fluid flows in contact with a surface from which they can detach and reattach. These problems are of particular importance in glaciology, where they arise in the study of grounding…

Numerical Analysis · Mathematics 2022-04-06 Gonzalo G. de Diego , Patrick E. Farrell , Ian J. Hewitt

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

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic fluid shell. The fluid motion is governed by the Navier-Stokes equations, while the fluid shell is modeled…

Analysis of PDEs · Mathematics 2007-05-23 C. H. Arthur Cheng , Daniel Coutand , Steve Shkoller

Motivated by extrusion problems, we consider a non-stationary incompress-ible 3D fluid flow with a non-constant (temperature dependent) viscosity, subjected to mixed boundary conditions with a given time dependent velocity on a part of the…

Analysis of PDEs · Mathematics 2015-12-22 Mahdi Boukrouche , Imane Boussetouan , Laetitia Paoli

We propose a variational framework for the resolution of a non-hydrostatic Saint-Venant type model with bottom topography. This model is a shallow water type approximation of the incompressible Euler system with free surface and slightly…

Numerical Analysis · Mathematics 2015-07-01 N. Aissiouene , M. -O. Bristeau , E. Godlewski , J. Sainte-Marie

A microscopic model able to describe simultaneously the dynamic viscosity and the self-diffusion coefficient of fluids is presented. This model is shown to emerge from the introduction of fractional calculus in a usual model of condensed…

Statistical Mechanics · Physics 2021-11-24 F. Aitken , F. Volino

We study a nonlinear, moving boundary fluid-structure interaction problem between an incompressible, viscous Newtonian fluid, modeled by the 2D Navier-Stokes equations, and an elastic structure modeled by the shell or plate equations. The…

Analysis of PDEs · Mathematics 2016-03-07 Boris Muha , Suncica Canic

In this paper, we investigate the magnetohydrodynamic viscous flow with second order slip flow model over a permeable shrinking surface. We have obtained the closed form of exact solution of Navier-Stokes equations by using similarity…

Fluid Dynamics · Physics 2016-06-28 T. Mahmood , S. Munawar Shah , G. Abbas

This is the second of two papers devoted to the asymptotic behavior of solutions to the incompressible Navier-Stokes equations in a half-space with point vortex initial data. A major difficulty stems from the interaction between the point…

Analysis of PDEs · Mathematics 2026-04-08 Chao Wang , Jingchao Yue , Zhifei Zhang

We study the motion of a compressible heat-conducting fluid in three dimensions interacting with a non-linear flexible shell. The fluid is described by the full Navier--Stokes--Fourier system. The shell constitutes an unknown part of the…

Analysis of PDEs · Mathematics 2021-11-18 Dominic Breit , Sebastian Schwarzacher

We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear…

Soft Condensed Matter · Physics 2015-04-24 S. Papenkort , Th. Voigtmann

We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…

Analysis of PDEs · Mathematics 2025-12-30 Andrea Giorgini , Jingning He , Hao Wu

We derive and justify a new effective model for a compressible viscous liquid-vapor flow on a spray-like scale, i.e., for settings with a large number of phase boundaries. As a model on the detailed scale, we start from a parabolic…

Analysis of PDEs · Mathematics 2025-12-18 Christian Rohde , Florian Wendt