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On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Martin Lanzendörfer, Jan Stebel (2011)

Applications of Mathematics

We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the traction at the inflow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and uniqueness of weak solutions (the latter for small data) and discuss particular applications of the results.

On quasi-stationary models of mixtures of compressible fluids

Jens Frehse, Wladimir Weigant (2008)

Applications of Mathematics

We consider mixtures of compressible viscous fluids consisting of two miscible species. In contrast to the theory of non-homogeneous incompressible fluids where one has only one velocity field, here we have two densities and two velocity fields assigned to each species of the fluid. We obtain global classical solutions for quasi-stationary Stokes-like system with interaction term.

On some free boundary problems for Navier-Stokes equations

Ewa Zadrzyńska (2005)

Banach Center Publications

In this survey we report on existence results for some free boundary problems for equations describing motions of both incompressible and compressible viscous fluids. We also present ways of controlling free boundaries in two cases: a) when the free boundary is governed by surface tension, b) when surface tension does not occur.

On stability of the P n mod / P n element for incompressible flow problems

Petr Knobloch (2006)

Applications of Mathematics

It is well known that finite element spaces used for approximating the velocity and the pressure in an incompressible flow problem have to be stable in the sense of the inf-sup condition of Babuška and Brezzi if a stabilization of the incompressibility constraint is not applied. In this paper we consider a recently introduced class of triangular nonconforming finite elements of n th order accuracy in the energy norm called P n elements. For n ≤ 3 we show that the stability condition holds if the velocity...

On suitable inlet boundary conditions for fluid-structure interaction problems in a channel

Jan Valášek, Petr Sváček, Jaromír Horáček (2019)

Applications of Mathematics

We are interested in the numerical solution of a two-dimensional fluid-structure interaction problem. A special attention is paid to the choice of physically relevant inlet boundary conditions for the case of channel closing. Three types of the inlet boundary conditions are considered. Beside the classical Dirichlet and the do-nothing boundary conditions also a generalized boundary condition motivated by the penalization prescription of the Dirichlet boundary condition is applied. The fluid flow...

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