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An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
This paper addresses the floating body problem which consists in studying the interaction of surface water waves with a floating body. We propose a new formulation of the water waves problem that can easily be generalized in order to take…
We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. Both gravity forces and surface tension are taken int account. A time-dependent conformal…
We consider the free boundary problem for non-relativistic and relativistic ideal compressible magnetohydrodynamics in two and three spatial dimensions with the total pressure vanishing on the plasma--vacuum interface. We establish the…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
We study the thermodynamics and non-relativistic hydrodynamics of the holographic fluid on a finite cutoff surface in the Gauss-Bonnet gravity. It is shown that the isentropic flow of the fluid is equivalent to a radial component of…
The fluid models mentioned in the title are studied in a modified approach, based on two formulas for the mass function. All characteristics of the fluid are expressed through a master potential, satisfying an ordinary second order…
This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier--Stokes equations expressed in…
We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds c {\in}]c*,…
We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken.…
The relativistic kinetic equations for the two domains separated by the hypersurface with both space- and time-like parts are derived. The particle exchange between the domains separated by the time-like boundaries generates source terms…
A model of unsteady filtration (seepage) in a porous medium with capillary retention is considered. It leads to a free boundary problem for a generalized porous medium equation where the location of the boundary of the water mound is…
We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely…
We prove that, in a two-dimensional strip, a steady flow of an ideal incompressible fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half-plane. The…
The purpose of this communication is to discuss the simulation of a free surface compressible flow between two fluids, typically air and water. We use a two fluid model with the same velocity, pressure and temperature for both phases. In…
Some features of the calculation of fluid dynamo systems in magnetohydrodynamics are studied. In the coupled set of the ordinary linear differential equations for the spherically symmetric $\alpha^2-$dynamos, the problem represented by the…
We investigate the master nonlinear partial differential equation that governs the evolution of shear-free spherically symmetric charged fluids. We use an approach which has not been considered previously for the underlying equation in…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…