The paper studies the interaction of a periodic solid bristle structure with a fluid. Such problems arise, for example, when modelling biotechnological devices operating in liquids or when simulating epithelium surfaces of blood vessels. The fluid is described by the linearized Navier– Stokes equation whereas the solid part is governed by equations of linear elasticity. The interface conditions...

Porous materials are present in many natural as well as engineered structures. Engineering examples include filters, sanitary products and foams while examples of natural occurrences are oil reservoirs and biological tissue. These materials possess a strongly heterogeneous microstructure consisting of a contiguous solid skeleton, more or less saturated with fluid. The scale of the substructural...

A recently reported symmetry breaking of density profiles of fluid argon confined by two parallel solid walls of carbon dioxide is studied. The calculations are performed in the framework of a nonlocal density functional theory. It is shown that the existence of such asymmetrical solutions is restricted to a special choice for the adsorption potential, where the attraction of the solid-fluid in...

The present work deals with continuum mechanical considerations for deformable and rigid solids as well as for fluids. A common finite element framework is used to approximate all systems under considerations. In particular, we present a standard displacement based formulation for the deformable solids and make use of this framework for the transition of the solid to a rigid body in the limit o...

Despite recent findings [1] on the superiority of monolithic approaches to FSI over the segregated ones, there are many advantages that make the latter a valuable alternative [2]. For example, in a staggered approach, individual solution strategies can be employed independently to fluid flow and solid dynamics and they can be coupled through a robust interface coupling methods. This allows rese...

We study the finite-horizon optimal control problem with quadratic functionals for an established fluid-structure interaction model. The coupled PDE system under investigation comprises a parabolic (the fluid) and a hyperbolic (the solid) dynamics; the coupling occurs at the interface between the regions occupied by the fluid and the solid. We establish several trace regularity results for the ...

We develop a combined field formulation for the fluid structure (FS) interaction problem. The unknowns are (u; p;v), being the fluid velocity, fluid pressure and solid velocity. This combined field formulation uses Arbitrary Lagrangian Eulerian (ALE) description for the fluid and Lagrangian description for the solid. It automatically enforces the simultaneous continuities of both velocity and t...

We study a fluid-structure interaction problem describing movement of rigid body inside bounded domain filled by viscous fluid. The fluid is modelled the generalized incompressible Naiver–Stokes equations which include cases Newtonian and non-Newtonian fluids. are coupled via Navier slip boundary conditions balance forces at fluid-rigid interface. Our analysis also includes case nonlinear condi...

There is no doubt that atherosclerosis is one of the most important health problems in the Western Societies. It is well accepted that atherosclerosis is associated with abnormal stress and strain conditions. A compelling observation is that the epicardial arteries develop atherosclerosis while the intramural arteries do not. Atherosclerotic changes involving the epicardial portion of the coron...