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.
Chérif Amrouche, Patrick Penel, Nour Seloula (2013)
Annales mathématiques Blaise Pascal
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This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.
Jiří Neustupa, Patrick Penel (2008)
Banach Center Publications
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We formulate a boundary value problem for the Navier-Stokes equations with prescribed u·n, curl u·n and alternatively (∂u/∂n)·n or curl²u·n on the boundary. We deal with the question of existence of a steady weak solution.
Roger Temam, Xiaoming Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Yoshiyuki Kagei, Takayuki Kobayashi (2005)
Banach Center Publications
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Paweł Konieczny (2008)
Banach Center Publications
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The paper analyzes the issue of existence of solutions to linear problems in two dimensional exterior domains, linearizations of the Navier-Stokes equations. The systems are studied with a slip boundary condition. The main results prove the existence of distributional solutions for arbitrary data.
Burda, Pavel, Novotný, Jaroslav, Šístek, Jakub
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We present analytical solution of the Stokes problem in 2D domains. This is then used to find the asymptotic behavior of the solution in the vicinity of corners, also for Navier-Stokes equations in 2D. We apply this to construct very precise numerical finite element solution.
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...