English
Related papers

Related papers: A Lagrange multiplier formulation for the fully dy…

200 papers

We present a novel formulation for parametric finite element methods to approximate two-phase Stokes flow. The new formulation is based on the classical Stokes equation in the bulk and a novel choice of interface conditions with additional…

Numerical Analysis · Mathematics 2025-08-19 Harald Garcke , Dennis Trautwein , Ganghui Zhang

We consider the interaction between an incompressible, viscous fluid modeled by the dynamic Stokes equation and a multilayered poroelastic structure which consists of a thin, linear, poroelastic plate layer (in direct contact with the free…

Analysis of PDEs · Mathematics 2021-08-17 Lorena Bociu , Sunčica Čanić , Boris Muha , Justin T. Webster

This paper presents a rigorous derivation of an effective model for fluid flow through a thin elastic porous membrane separating two fluid bulk domains. The microscopic setting involves a periodically structured porous membrane composed of…

Analysis of PDEs · Mathematics 2025-08-07 Markus Gahn , Maria Neuss-Radu

Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…

Fluid Dynamics · Physics 2015-08-13 François Laenen , Giorgio Krstulovic , Jérémie Bec

We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of…

Analysis of PDEs · Mathematics 2020-10-05 Sebastian Schwarzacher , Matthias Sroczinski

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

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and…

Fluid Dynamics · Physics 2019-05-01 Lianlei Lin , Suchuan Dong

In this work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. By a variational approach we show…

Analysis of PDEs · Mathematics 2022-01-12 B. Benesova , M. Kampschulte , S. Schwarzacher

We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works,…

Analysis of PDEs · Mathematics 2026-03-13 Antonín Češík , Malte Kampschulte , Sebastian Schwarzacher

We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…

Numerical Analysis · Mathematics 2023-06-21 Harald Garcke , Robert Nürnberg , Quan Zhao

We consider the dynamics of two-phase fluids, in particular the moving contact line, on a solid substrate. The dynamics are governed by the sharp-interface model consisting of the incompressible Navier-Stokes\slash Stokes equations with the…

Computational Physics · Physics 2020-07-15 Quan Zhao , Weiqing Ren

We derive a continuum sharp-interface model for moving contact lines with soluble surfactants in a thermodynamically consistent framework. The model consists of the isothermal two-phase incompressible Navier-Stokes equations for the fluid…

Fluid Dynamics · Physics 2021-08-11 Quan Zhao , Weiqing Ren , Zhen Zhang

In this paper, we propose a numerical method for computing solutions to Biot's fully dynamic model of incompressible saturated porous media [Biot;1956]. Our spatial discretization scheme is based on the three-field formulation (u-w-p) and…

Numerical Analysis · Mathematics 2015-06-24 Zahrasadat Lotfian , Mettupalayam Sivaselvan

The basal sliding of glaciers and ice sheets can constitute a large part of the total observed ice velocity, in particular in dynamically active areas. It is therefore important to accurately represent this process in numerical models. The…

Computational Physics · Physics 2019-07-30 Christian Helanow

We investigate the fluid-poroelastic structure interaction problem in a moving domain, governed by Navier-Stokes-Biot (NSBiot) system. First, we propose a fully parallelizable, loosely coupled scheme to solve the coupled system. At each…

Numerical Analysis · Mathematics 2024-09-25 Shihan Guo , Yizhong Sun , Yifan Wang , Xiaohe Yue , Haibiao Zheng

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A…

Numerical Analysis · Mathematics 2023-06-27 Wietse M. Boon , Martin Hornkjøl , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…

Analysis of PDEs · Mathematics 2022-06-08 Miroslav Bulíček , Josef Málek , Casey Rodriguez

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

The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in $\mathbb{R}^3$. For the resulting Navier-Stokes type system, posed on a smooth closed…

Analysis of PDEs · Mathematics 2022-03-04 Maxim A. Olshanskii , Arnold Reusken , Alexander Zhiliakov