Displaying similar documents to “A direct boundary integral method for a mobility problem.”

Finite differences and boundary element methods for non-stationary viscous incompressible flow

Werner Varnhorn (1994)

Banach Center Publications

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We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation...

Convergence of the rotating fluids system in a domain with rough boundaries

David Gérard-Varet (2003)

Journées équations aux dérivées partielles

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We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size ϵ . We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as ϵ goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with...

On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid

Ewa Zadrzyńska, Wojciech M. Zajączkowski (1996)

Annales Polonici Mathematici

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We consider the motion of a viscous compressible heat conducting fluid in ℝ³ bounded by a free surface which is under constant exterior pressure. Assuming that the initial velocity is sufficiently small, the initial density and the initial temperature are close to constants, the external force, the heat sources and the heat flow vanish, we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.

Non-parallel plane Rayleigh Benard convection in cylindrical geometry

A. Golbabai (1995)

Applicationes Mathematicae

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This paper considers the effect of a perturbed wall in regard to the classical Benard convection problem in which the lower rigid surface is of the form z = ε 2 g ( s ) , s=ε r, in axisymmetric cylindrical polar coordinates (r,ϕ,z). The boundary conditions at s=0 for the linear amplitude equation are found and it is shown that these conditions are different from those which apply to the nonlinear problem investigated by Brown and Stewartson [1], representing the distribution of convection cells near...

On a non-stationary free boundary transmission problem with continuous extraction and convection, arising in industrial processes

Bui Ton, Grzegorz Łukaszewicz (1992)

Banach Center Publications

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The existence of a weak solution of a non-stationary free boundary transmission problem arising in the production of industrial materials is established. The process is governed by a coupled system involving the Navier--Stokes equations and a non-linear heat equation. The stationary case was studied in [7].

Some remarks to the compactness of steady compressible isentropic Navier-Stokes equations via the decomposition method

Antonín Novotný (1996)

Commentationes Mathematicae Universitatis Carolinae

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In [18]–[19], P.L. Lions studied (among others) the compactness and regularity of weak solutions to steady compressible Navier-Stokes equations in the isentropic regime with arbitrary large external data, in particular, in bounded domains. Here we investigate the same problem, combining his ideas with the method of decomposition proposed by Padula and myself in [29]. We find the compactness of the incompressible part u of the velocity field v and we give a new proof of the compactness...