1st Edition

Computational Fluid Dynamics

Edited By Frederic Magoules Copyright 2012
    407 Pages 124 B/W Illustrations
    by Chapman & Hall

    408 Pages 124 B/W Illustrations
    by Chapman & Hall

    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.

    Finite Volumes Methods, Jérôme Boudet
    Introduction
    Conservativity
    Control volume integration
    Grid
    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
    Introduction
    Principles of the weighted residuals method
    Collocation or pseudo-spectral method
    Least squares method
    Method of moments
    Galerkin approximation
    Subdomains
    An example

    Spectral Methods, Fabien Godeferd
    Introduction
    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
    Introduction
    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
    Introduction
    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
    Introduction
    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
    Introduction
    Numerical model
    Large eddy simulation (LES)
    Variational multiscale large eddy simulation (VMS-LES)
    Hybrid RANS/LES
    Concluding remarks

    Numerical Algorithms for Free Surface Flow, Alexandre Caboussat, Guillaume Jouvet, Marco Picasso, and Jacques Rappaz
    Introduction
    A short review on two-phases flow with free surfaces
    Some preliminary remarks on ice and glacier modeling
    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

    Bibliography

    Biography

    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).