Displaying similar documents to “Linear flow problems in 2D exterior domains for 2D incompressible fluid flows”

On the structure of flows through pipe-like domains satisfying a geometrical constraint

Piotr Bogusław Mucha (2004)

Applicationes Mathematicae

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We study solutions of the steady Navier-Stokes equations in a bounded 2D domain with the slip boundary conditions admitting flow across the boundary. We show conditions guaranteeing uniqueness of the solution. Next, we examine the structure of the solution considering an approximation given by a natural linearization. Suitable error estimates are also obtained.

Analytical solution of rotationally symmetric Stokes flow near corners

Burda, Pavel, Novotný, Jaroslav, Šístek, Jakub

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We present analytical solution of the Stokes problem in rotationally symmetric domains. This is then used to find the asymptotic behaviour of the solution in the vicinity of corners, also for Navier-Stokes equations. We apply this to construct very precise numerical finite element solution.

Global existence for the inflow-outflow problem for the Navier-Stokes equations in a cylinder

Piotr Kacprzyk (2009)

Applicationes Mathematicae

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Global existence of regular solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe with large inflow and outflow is shown. To prove the long time existence we need smallness of derivatives, with respect to the variable along the axis of the cylinder, of the external force and of the initial velocity in L₂-norms. Moreover, we need smallness of derivatives of inflow and outflow with respect to tangent directions to the boundary...

Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations

Charles-Henri Bruneau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Non reflecting boundary conditions on artificial frontiers of the domain are proposed for both incompressible and compressible Navier-Stokes equations. For incompressible flows, the boundary conditions lead to a well-posed problem, convey properly the vortices without any reflections on the artificial limits and allow to compute turbulent flows at high Reynolds numbers. For compressible flows, the boundary conditions convey properly the vortices without any reflections on the artificial...

On the existence of pullback attractor for a two-dimensional shear flow with Tresca's boundary condition

Mahdi Boukrouche, Grzegorz Łukaszewicz (2008)

Banach Center Publications

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We consider a two-dimensional Navier-Stokes shear flow with time dependent boundary driving and subject to Tresca law. We establish the existence of a unique global in time solution and then, using a recent method based on the concept of the Kuratowski measure of noncompactness of a bounded set, we prove the existence of the pullback attractor for the associated cocycle. This research is motivated by a problem from lubrication theory.