Related papers: A review on rigorous derivation of reduced models …
We analyze a linear 3D/3D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic plate-like structure with the aim of deriving a simplified reduced model. Based on suitable energy dissipation…
Starting from a nonlinear 2D/1D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic structure, on the vanishing limit of the relative fluid thickness, we rigorously derive a sixth-order thin-film…
A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A…
Fluid-structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid-structure interaction model for…
We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical…
Using group theoretical methods, we analyze the generalization of a one-dimensional sixth-order thin film equation which arises in considering the motion of a thin film of viscous fluid driven by an overlying elastic plate. The most general…
We use dynamical systems theory to construct the normal form of the Navier--Stokes equations for the flow of a thin layer of fluid upon a solid substrate. The normal form equations illuminate the fluid dynamics by decoupling the long-term…
We introduce optimization-based full-order and reduced-order formulations of fluid structure interaction problems. We study the flow of an incompressible Newtonian fluid which interacts with an elastic body: we consider an arbitrary…
This work presents a mathematical model for the optimal control of thin-film flows over a flexible topography influenced by an external force. Our thin-film model allows for the rupture of films as well as the coalescence of bubbles. The…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…
We propose a two-fold approach to model reduction of fluid-structure interaction. The state equations for the fluid are solved with reduced basis methods. These are model reduction methods for parametric partial differential equations using…
Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order…
We derive a thin film model for viscoelastic liquids under strong slip which obey the stress tensor dynamics of corotational Jeffreys fluids.
Thin film rupture is a type of nonlinear instability that causes the solution to touch down to zero at finite time. We investigate the finite-time rupture behavior of a generalized elastohydrodynamic lubrication model. This model features…
We study the interaction between incompressible viscous fluids and multilayered elastic structures in a 3D/2D/3D framework, where a 3D fluid interacts with a 2D thin elastic layer, coupled to a 3D thick elastic solid. The system is driven…
We consider a two-dimensional motion of a thin film flowing down an inclined plane under the influence of the gravity and the surface tension. In order to investigate the stability of such flow, we often use a thin film approximation, which…
A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…
We derive several lubrication approximation models, using Shikhmurzaev's approach to the contact line problem, obtained in \cite{GNV}. The first two lubrication models describe thin film flow of incompressible fluids on solid substrates,…