Displaying similar documents to “Governing equations of fluid mechanics in physical curvilinear coordinate system.”

Vorticity dynamics and numerical resolution of Navier-Stokes equations

Matania Ben-Artzi, Dalia Fishelov, Shlomo Trachtenberg (2001)

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

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We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical...

Numerical approximation of flow in a symmetric channel with vibrating walls

Sváček, Petr, Horáček, Jaromír

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In this paper the numerical solution of two dimensional fluid-structure interaction problem is addressed. The fluid motion is modelled by the incompressible unsteady Navier-Stokes equations. The spatial discretization by stabilized finite element method is used. The motion of the computational domain is treated with the aid of Arbitrary Lagrangian Eulerian (ALE) method. The time-space problem is solved with the aid of multigrid method. The method is applied onto a problem of interaction...

Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 2. Contributions to the June 2004 conference

Henri Paillère, Patrick Le Quéré, Catherine Weisman, Jan Vierendeels, Erik Dick, Malte Braack, Frédéric Dabbene, Alberto Beccantini, Etienne Studer, Thibaud Kloczko, Christophe Corre, Vincent Heuveline, Masoud Darbandi, Seyed Farid Hosseinizadeh (2005)

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

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In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.

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...

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...

On fully developed flows of fluids with a pressure dependent viscosity in a pipe

Macherla Vasudevaiah, Kumbakonam R. Rajagopal (2005)

Applications of Mathematics

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Stokes recognized that the viscosity of a fluid can depend on the normal stress and that in certain flows such as flows in a pipe or in channels under normal conditions, this dependence can be neglected. However, there are many other flows, which have technological significance, where the dependence of the viscosity on the pressure cannot be neglected. Numerous experimental studies have unequivocally shown that the viscosity depends on the pressure, and that this dependence can be quite...

Medical image – based computational model of pulsatile flow in saccular aneurisms

Stéphanie Salmon, Marc Thiriet, Jean-Frédéric Gerbeau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...