Computational Fluid Dynamics: 1st Edition (Paperback) book cover

Computational Fluid Dynamics

1st Edition

Edited by Frederic Magoules

Chapman and Hall/CRC

407 pages | 124 B/W Illus.

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Exploring new variations of classical methods as well as recent approaches appearing in the field, Computational Fluid Dynamics demonstrates the extensive use of numerical techniques and mathematical models in fluid mechanics. It presents various numerical methods, including finite volume, finite difference, finite element, spectral, smoothed particle hydrodynamics (SPH), mixed-element-volume, and free surface flow.

Taking a unified point of view, the book first introduces the basis of finite volume, weighted residual, and spectral approaches. The contributors present the SPH method, a novel approach of computational fluid dynamics based on the mesh-free technique, and then improve the method using an arbitrary Lagrange Euler (ALE) formalism. They also explain how to improve the accuracy of the mesh-free integration procedure, with special emphasis on the finite volume particle method (FVPM). After describing numerical algorithms for compressible computational fluid dynamics, the text discusses the prediction of turbulent complex flows in environmental and engineering problems. The last chapter explores the modeling and numerical simulation of free surface flows, including future behaviors of glaciers.

The diverse applications discussed in this book illustrate the importance of numerical methods in fluid mechanics. With research continually evolving in the field, there is no doubt that new techniques and tools will emerge to offer greater accuracy and speed in solving and analyzing even more fluid flow problems.

Table of Contents

Finite Volumes Methods, Jérôme Boudet



Control volume integration


General flux interpolation

Resolution and time discretization

Consistency, stability, and convergence

Upwind interpolation

Particular case of structured grids

Boundary conditions

Weighted Residuals Methods, Fabien Godeferd


Principles of the weighted residuals method

Collocation or pseudo-spectral method

Least squares method

Method of moments

Galerkin approximation


An example

Spectral Methods, Fabien Godeferd


Linear problem: Galerkin, tau, and collocation methods

Applications: Fourier

Applications: Chebyshev

Implicit equations

Evaluation of nonlinear terms

Smoothed-Particle Hydrodynamics (SPH) Methods, Francis Leboeuf and Jean-Christophe Marongiu


SPH approximation of a function

Properties of the kernel function W

Barycenter of D(xi)

Choices of the kernel function W

SPH approximation of differential operators applied on a function ø

Using a Taylor series expansion

Concluding remarks

Application of SPH Methods to Conservation Equations, Francis Leboeuf and Jean-Christophe Marongiu

General form of conservation equation

Weak SPH-ALE formulation of the conservation equations

Application to flow conservation equations

Boundary conditions

Applications of SPH and SPH-ALE methods

Finite Volume Particle Methods (FVPM), Francis Leboeuf and Jean-Christophe Marongiu


Partition of unity

Average of a function ø

Derivatives of ψ

Conservation equation and FVPM

Concluding remarks

Numerical Algorithms for Unstructured Meshes, Bruno Koobus, Frédéric Alauzet, and Alain Dervieux


Spatial representation

Toward higher spatial order

Positivity of mixed element-volume formulations

3D multi-scales anisotropic mesh adaptation

3D goal-oriented anisotropic mesh adaptation

Concluding remarks

LES, Variational Multiscale LES, and Hybrid Models, Hilde Ouvrard, Maria-Vittoria Salvetti, Simone Camarri, Stephen Wornom, Alain Dervieux, and Bruno Koobus


Numerical model

Large eddy simulation (LES)

Variational multiscale large eddy simulation (VMS-LES)


Concluding remarks

Numerical Algorithms for Free Surface Flow, Alexandre Caboussat, Guillaume Jouvet, Marco Picasso, and Jacques Rappaz


A short review on two-phases flow with free surfaces

Some preliminary remarks on ice and glacier modeling


Time splitting scheme

A two-grids method for space discretization

Modeling of interfacial effects

Numerical results for liquid flow

Numerical results for ice flow

Concluding remarks


About the Editor

Frédéric Magoulès is a professor in the Applied Mathematics and Systems Laboratory at École Centrale Paris. He is the editor of Fundamentals of Grid Computing: Theory, Algorithms and Technologies (CRC Press, December 2009), co-author of Introduction to Grid Computing (CRC Press, March 2009), and co-author of Grid Resource Management: Toward Virtual and Services Compliant Grid Computing (CRC Press, September 2008).

About the Series

Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Number Systems
SCIENCE / Physics