Computational Fluid Dynamics  book cover
1st Edition

Computational Fluid Dynamics

Edited By

Frederic Magoules

ISBN 9781138382091
Published September 18, 2018 by Chapman and Hall/CRC
407 Pages 124 B/W Illustrations

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Book Description

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


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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).