A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A finite element method to solve the bidimensional Reduced Navier-Stokes Prandtl (RNS/P) equations is described. These equations are an asymptotical simplification of the full Navier-Stokes equations, obtained when one dimension of the domain is of one order smaller than the others. These aretherefore of particular interest to describe flows in channels or pipes of small diameter. A low order finite element discretization, based on a piecewise constant approximation of the pressure, is proposed and analyzed. Numerical experiments which consist in fluid flow simulations within a constricted pipe are provided. Comparisons with Navier-Stokes simulations allow to evaluate the performance of prediction of the finite element method, and of the model itself.
Language English 54-68 15 Zeitschrift fur Angewandte Mathematik und Mechanik 89 1 10.1002/zamm.200800068 Published - 16 Jan 2009

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Navier-Stokes
Finite Element Method
Pipe
Finite element method
Flow simulation
Flow Simulation
Finite Element Discretization
Simplification
One Dimension
Navier Stokes equations
Fluid Flow
Flow of fluids
Navier-Stokes Equations
Numerical Experiment
Evaluate
Prediction
Approximation
Simulation
Experiments
Model

Keywords

• incompressible flow
• RNS/P equations
• finite elements

Cite this

title = "A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations",
abstract = "A finite element method to solve the bidimensional Reduced Navier-Stokes Prandtl (RNS/P) equations is described. These equations are an asymptotical simplification of the full Navier-Stokes equations, obtained when one dimension of the domain is of one order smaller than the others. These aretherefore of particular interest to describe flows in channels or pipes of small diameter. A low order finite element discretization, based on a piecewise constant approximation of the pressure, is proposed and analyzed. Numerical experiments which consist in fluid flow simulations within a constricted pipe are provided. Comparisons with Navier-Stokes simulations allow to evaluate the performance of prediction of the finite element method, and of the model itself.",
keywords = "incompressible flow, RNS/P equations, finite elements",
author = "Barrenechea, {Gabriel R.} and Franz Chouly",
year = "2009",
month = "1",
day = "16",
doi = "10.1002/zamm.200800068",
language = "English",
volume = "89",
pages = "54--68",
journal = "Zeitschrift fur Angewandte Mathematik und Mechanik",
issn = "0044-2267",
number = "1",

}

In: Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 89, No. 1, 16.01.2009, p. 54-68.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations

AU - Barrenechea, Gabriel R.

AU - Chouly, Franz

PY - 2009/1/16

Y1 - 2009/1/16

N2 - A finite element method to solve the bidimensional Reduced Navier-Stokes Prandtl (RNS/P) equations is described. These equations are an asymptotical simplification of the full Navier-Stokes equations, obtained when one dimension of the domain is of one order smaller than the others. These aretherefore of particular interest to describe flows in channels or pipes of small diameter. A low order finite element discretization, based on a piecewise constant approximation of the pressure, is proposed and analyzed. Numerical experiments which consist in fluid flow simulations within a constricted pipe are provided. Comparisons with Navier-Stokes simulations allow to evaluate the performance of prediction of the finite element method, and of the model itself.

AB - A finite element method to solve the bidimensional Reduced Navier-Stokes Prandtl (RNS/P) equations is described. These equations are an asymptotical simplification of the full Navier-Stokes equations, obtained when one dimension of the domain is of one order smaller than the others. These aretherefore of particular interest to describe flows in channels or pipes of small diameter. A low order finite element discretization, based on a piecewise constant approximation of the pressure, is proposed and analyzed. Numerical experiments which consist in fluid flow simulations within a constricted pipe are provided. Comparisons with Navier-Stokes simulations allow to evaluate the performance of prediction of the finite element method, and of the model itself.

KW - incompressible flow

KW - RNS/P equations

KW - finite elements

U2 - 10.1002/zamm.200800068

DO - 10.1002/zamm.200800068

M3 - Article

VL - 89

SP - 54

EP - 68

JO - Zeitschrift fur Angewandte Mathematik und Mechanik

T2 - Zeitschrift fur Angewandte Mathematik und Mechanik

JF - Zeitschrift fur Angewandte Mathematik und Mechanik

SN - 0044-2267

IS - 1

ER -