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We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type. This leads to a coupled system of non-linear PDEs where the moving part of the boundary is an…

Analysis of PDEs · Mathematics 2022-11-15 Boris Muha , Sebastian Schwarzacher

In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…

Analysis of PDEs · Mathematics 2019-12-24 Yang Li , Ewelina Zatorska

We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with…

Fluid Dynamics · Physics 2016-10-05 Andres Goza , Tim Colonius

We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic…

Analysis of PDEs · Mathematics 2021-07-28 V. Kozlov , S. Nazarov , G. Zavorokhin

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

We study a novel approach for the existence of solutions to an incompressible fluid-rigid body interaction problem in three dimensions. Our approach introduces an iteration based on a sequence of related problems posed on domains with…

Numerical Analysis · Mathematics 2026-01-21 Charles M. Elliott , Thomas Sales

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of central importance in detecting and identifying submerged objects. The problem is generally referred to…

Numerical Analysis · Mathematics 2014-06-10 George C. Hsiao , Francisco-Javier Sayas , Richard J. Weinacht

We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

Analysis of PDEs · Mathematics 2025-06-23 Alex Doak , Karsten Matthies , Jonathan Sewell , Miles H. Wheeler

In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position…

Analysis of PDEs · Mathematics 2019-05-27 Ondrej Kreml , Sarka Necasova , Tomasz Piasecki

This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…

Analysis of PDEs · Mathematics 2023-06-28 David Lannes , Tatsuo Iguchi

This paper presents a numerical method for the simulation of fluid-structure interaction specifically tailored to interactions between Newtonian fluids and a large number of slender viscoelastic Cosserat rods. Because of their high…

Soft Condensed Matter · Physics 2022-01-13 S. Tschisgale , J. Fröhlich

Many-body interactions can play a relevant role in water properties. Here we study by Monte Carlo simulations a coarse-grained model for bulk water that includes many-body interactions associated to water cooperativity. The model is…

Statistical Mechanics · Physics 2016-10-04 Luis Enrique Coronas , Valentino Bianco , Arne Zantop , Giancarlo Franzese

In recent years, slippery surfaces have attracted significant interest due to their excellent liquid-repellent properties and their potential in diverse commercial applications. Such surfaces are prepared by coating functionalized solid…

Soft Condensed Matter · Physics 2026-05-25 Shivam Gupta , Bidisha Bhatt , Zhaohe Dai , Krishnacharya Khare

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

In this study, we investigate the dynamics of particles overcoming the hydrodynamic barrier posed by a thin fluid film to achieve contact in finite time, a phenomenon critical in various natural and engineered processes such as enzyme…

Fluid Dynamics · Physics 2024-08-06 John Sebastian , Alexander L. Schødt , Kaare H. Jensen

The stability of flows in layers of finite thickness $H$ is examined against small scale three dimensional (3D) perturbations and large scale two-dimensional (2D) perturbations. The former provide an indication of a forward transfer of…

Fluid Dynamics · Physics 2018-06-04 Alexandros Alexakis

Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…

Analysis of PDEs · Mathematics 2026-01-30 Stanislav Mosny , Boris Muha , Sebastian Schwarzacher , Justin T. Webster

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

In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…

We consider a fluid-structure interaction system composed by a rigid ball immersed into a viscous incompressible fluid. The motion of the structure satisfies the Newton laws and the fluid equations are the standard Navier-Stokes system. At…

Analysis of PDEs · Mathematics 2019-12-06 Matthieu Hillairet , Takéo Takahashi