Related papers: The solid-fluid transmission problem
We study the isotropic elastic wave equation in a bounded domain with boundary with coefficients having jumps at a nested set of interfaces satisfying the natural transmission conditions there. We analyze in detail the microlocal behavior…
A coupled system composed of a Newtonian fluid located on a sinusoidally-forced elastic solid is studied analytically and numerically. The focus is on the transient evolution from the beginning of the forced oscillations and on the periodic…
Several methods for handling sloping fluid-solid interfaces with the elastic parabolic equation are tested. A single-scattering approach that is modified for the fluid-solid case is accurate for some problems but breaks down when the…
We consider two-layers of immiscible liquids confined between an upper and a lower rigid plate. The dynamics of the free liquid-liquid interface is described for arbitrary amplitudes by a single evolution equation derived from the basic…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
A comprehensive review of current analytical models, experimental techniques, and influencing factors is carried out to highlight the current challenges in this area. The study of fluid-solid boundary conditions has been ongoing for more…
A pressure driven flow in contact interface between elastic solids with wavy surfaces is studied. We consider a strong coupling between the solid and the fluid problems, which is relevant when the fluid pressure is comparable with the…
This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded…
The floating structure problem describes the interaction between surface water waves and a floating body, generally a boat or a wave energy converter. As shown by Lannes in [18] the equations for the fluid motion can be reduced to a set of…
In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
The development of microfluidic devices has recently revived the interest in "old" problems associated with transport at, or across, interfaces. As the characteristic sizes are decreased, the use of pressure gradients to transport fluids…
In this work we study the evolution of the interface between two different fluids in two concentric cylinders when the velocity is given by the Navier-Stokes equation and one of the fluids is thin. We present a formal asymptotic derivation…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…
A general adsorption model is developed to describe the interactions between near-wall fluid molecules and solid surface. This model serves as a framework for the theoretical modelling of the boundary slip phenomena. Based on this…
We study dispersive models of fluid flow in viscoelastic vessels, derived in the study of blood flow. The unknowns in the models are the velocity of the fluid in the axial direction and the displacement of the vessel wall from rest. We…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem,…
This paper is concerned with the diffusion of a fluid through a viscoelastic solid undergoing large deformations. Using ideas from the classical theory of mixtures and a thermodynamic framework based on the notion of maximization of the…
We are concerned with a coupled-physics spectral problem arising in the coupled propagation of acoustic and elastic waves, which is referred to as the acoustic-elastic transmission eigenvalue problem. There are two major contributions in…