Displaying similar documents to “Finite element solution of Navier-Stokes equations in shallow domains”

An application of the BDDC method to the Navier-Stokes equations in 3-D cavity

Hanek, Martin, Šístek, Jakub, Burda, Pavel

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We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient...

On mathematical modelling of gust response using the finite element method

Sváček, Petr, Horáček, Jaromír

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In this paper the numerical approximation of aeroelastic response to sudden gust is presented. The fully coupled formulation of two dimensional incompressible viscous fluid flow over a flexibly supported structure is used. The flow is modelled with the system of Navier-Stokes equations written in Arbitrary Lagrangian-Eulerian form and coupled with system of ordinary differential equations describing the airfoil vibrations with two degrees of freedom. The Navier-Stokes equations are spatially...

Isogeometric analysis for fluid flow problems

Bastl, Bohumír, Brandner, Marek, Egermaier, Jiří, Michálková, Kristýna, Turnerová, Eva

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The article is devoted to the simulation of viscous incompressible fluid flow based on solving the Navier-Stokes equations. As a numerical model we chose isogeometrical approach. Primary goal of using isogemetric analysis is to be always geometrically exact, independently of the discretization, and to avoid a time-consuming generation of meshes of computational domains. For higher Reynolds numbers, we use stabilization techniques SUPG and PSPG. All methods mentioned in the paper are...

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.

Lagrangian approximations and weak solutions of the Navier-Stokes equations

Werner Varnhorn (2008)

Banach Center Publications

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The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles...

Linear flow problems in 2D exterior domains for 2D incompressible fluid flows

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.

Computation of the drag force on a sphere close to a wall

David Gérard-Varet, Matthieu Hillairet (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.

On the Qualitative Behavior of the Solutions to the 2-D Navier-Stokes Equation

M. Pulvirenti (2008)

Bollettino dell'Unione Matematica Italiana

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This talk, based on a research in collaboration with E. Caglioti and F.Rousset, deals with a modified version of the two-dimensional Navier-Stokes equation wich preserves energy and momentum of inertia. Such a new equation is motivated by the occurrence of different dissipation time scales. It is also related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics.