Computational Fluid Dynamics

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.

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).

Finite Volumes Methods, Jérôme Boudet Introduction ConservativityControl volume integrationGridGeneral flux interpolationResolution and time discretizationConsistency, stability, and convergenceUpwind interpolation Particular case of structured gridsBoundary conditions

Weighted Residuals Methods, Fabien GodeferdIntroductionPrinciples of the weighted residuals methodCollocation or pseudo-spectral methodLeast squares methodMethod of momentsGalerkin approximationSubdomainsAn example

Spectral Methods, Fabien GodeferdIntroduction Linear problem: Galerkin, tau, and collocation methods Applications: FourierApplications: Chebyshev Implicit equations Evaluation of nonlinear terms

Smoothed-Particle Hydrodynamics (SPH) Methods, Francis Leboeuf and Jean-Christophe MarongiuIntroduction SPH approximation of a functionProperties of the kernel function WBarycenter of D(xi)Choices of the kernel function WSPH approximation of differential operators applied on a function øUsing a Taylor series expansion Concluding remarks

Application of SPH Methods to Conservation Equations, Francis Leboeuf and Jean-Christophe MarongiuGeneral form of conservation equationWeak SPH-ALE formulation of the conservation equations Application to flow conservation equationsBoundary conditionsApplications of SPH and SPH-ALE methods

Finite Volume Particle Methods (FVPM), Francis Leboeuf and Jean-Christophe MarongiuIntroduction Partition of unityAverage of a function ø Derivatives of ψConservation equation and FVPMConcluding remarks

Numerical Algorithms for Unstructured Meshes, Bruno Koobus, Frédéric Alauzet, and Alain DervieuxIntroductionSpatial representation Toward higher spatial order Positivity of mixed element-volume formulations3D multi-scales anisotropic mesh adaptation3D goal-oriented anisotropic mesh adaptationConcluding remarks

LES, Variational Multiscale LES, and Hybrid Models, Hilde Ouvrard, Maria-Vittoria Salvetti, Simone Camarri, Stephen Wornom, Alain Dervieux, and Bruno KoobusIntroduction Numerical model Large eddy simulation (LES)Variational multiscale large eddy simulation (VMS-LES)Hybrid RANS/LESConcluding remarks

Numerical Algorithms for Free Surface Flow, Alexandre Caboussat, Guillaume Jouvet, Marco Picasso, and Jacques RappazIntroductionA short review on two-phases flow with free surfacesSome preliminary remarks on ice and glacier modeling Modeling Time splitting schemeA two-grids method for space discretizationModeling of interfacial effectsNumerical results for liquid flow Numerical results for ice flow Concluding remarks

Bibliography