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).
