méthodes asymptotiques, Méthodes d'échelles multiples, développements aymptotiques raccordés

Multiscale Hydrodynamic Phenomena:
Method of Matched Asymptotic Expansions,
Multiple Scale Analysis, Boundary Layers.

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Asymptotic Analysis in Paris




up to date 17 oct 2017
this page:  http://www.lmm.jussieu.fr/~lagree/COURS/M2MHP/index.html

les logos!!!




M2 MF2A P6 : Fluid Mechanics, M2 Fluid Mechanics : UPMC
MEC653 Multiscale hydrodynamic phenomena

first semester 2017-2018.
- 1 week free
- 1 week exam (Friday 2nd Dec.)
NSF01-Multiscale hydrodynamic phenomena
http://www.master.sdi.upmc.fr/modules/resources/download/gestionsdi/Mecanique/M2/M2-Mecanique_fluides/planningM2.MF2A.html



C01 F 29 september      08h30  11h00 F
C02 F 06 october      13h30  17h30
C03 F 13 october      08h30  12h30
C04 F 20 october      08h30  12h30
C05 T 24 october      08h30  12h30
C06 F 27 october      13h30  17h30
C00 F 03 november      freeeeee
C07 W 10 november      08h30   10h30 and 15h30  17h30
C00 F 17 november   FREE
C00 F 24 november   FREE
Dec 01 exam 08h30  12h00



Lecture  1:  10 oct 16
- simple introduction in the free-fall case  
- definition of asymptotic developments  
- simple example of singular problem
- Friedrich problem
- Friedrich 2nd order 
- another simple example the pipe with suction
- a non linear example: shocks and boundary layers
- the Logarithm case

download the file of introduction.
download the file of lecture 1 (in english).
download the file of lecture 1 (in french).


Books for these chapters:
Perturbation methods Hinch chapter 5
Perturbation methods in fluid mechanics M. Van Dyke chapter 3 and 5
Advanced Mathematical Methods for Scientists and Engineers Carl M. Bender, Steven A. Orszag, Chapter 7 and 9
Advanced Mathematical Methods for Scientists and Engineers Bender Orszag, Chapter 9
Méthodes Asymptotiques Mauss and Cousteix  
Asymptotic analysis and boundary layers Mauss and Cousteix  
Perturbation methods in fluid mechanics M. Van Dyke
Perturbation methods Hinch

Web:
scholarpedia
Hunter course




 
Lecture 2:  oct 06 2017
- Feymann averaging method
- Method of Averaging
- Multiple scale analysis
- WKB theory
- Example of the damped oscillator
- Example of Friedrich

download the file of lecture (I am sorry as this text is in french, but equations are in english).
download the file of dominant part of the lecture (in english).

Books for this chapter:
Perturbation methods Hinch chapter 7
Advanced Mathematical Methods for Scientists and Engineers: Carl M. Bender, Steven A. Orszag, chapter 10 and 11.
Advanced Mathematical Methods for Scientists and Engineers: Bender Orszag, Chapter 10-11
Perturbation methods J. Hinch  Cambridge University Press, (1991)
Méthodes Asymptotiques Mauss and Cousteix  
Asymptotic analysis and boundary layers Mauss and Cousteix  

Web:
scholarpedia



Lecture not in 2017:
- Lévêque & Graetz problems

download the file of lecture XX

Books for this chapter:
Hulin Petit Guyon Mitescu Physical Hydrodynamics page 421 for the  Lévêque solution
Schlichting Boundary Layer Theory McGrawHill
Pedley "Blood flow in large vessels"



Lecture  only heat equation in 2016:
- Self similar solutions

download the file (caution, explicit sexual content.)

Books for this chapter:
Grigory Isaakovich Barenblatt Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis cambridge 96
Bluman, G & Kumei, S, Symmetries and Differential Equations, Springer 1989, 412 pp (Vol. 81, Appl. Math. Sci; reprinted with corrections, 1996);
Sedov Similitude et Dimensions en Mécanique, MIR



Lecture 3: oct. 13 2017
- Ideal Fluid

download the file of lecture 3

Books for these chapters:
J. Kevorkian, J Cole, Perturbation methods in applied mathematics. Applied Mathematical Sciences, vol. 34, Springer-Verlag, Berlin and New York, 1981
but google book has new editions....
Landau Lifshitz, Fluid mechanics 
Germain Mécanique Tome II
Cousteix Books; Mauss Cousteix Books
Boundary Layer Theory Schlichting and Gersten



Lecture : 3 and 9 nov 2016
- Boundary Layer separation, Triple Deck
- Interactive Boundary Layer

download the file on triple deck and the file on IBL of lecture XX

Books for this chapters:
SteinruckAsymptotic Methods in Fluid Mechanics: Survey and Recent Advances
Schlichting Gersten and Schlichting Boundary Layer Theory
Modeling and computation of boundary-layer flows by Tuncer Cebeci, Jean Cousteix
Introduction to interactive boundary layer theory by Ian John Sobey
Asymptotic theory of separated flows by V. V.Sychev et al.




Lecture  9 nov 2016
- Small Reynolds fluid dynamics, Oseen.

download the file of lecture 3

Books for this chapter:
Perturbation methods in fluid mechanics M. Van Dyke chapter 8
fluid mechanics Kundu
Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder Proudman Pearson, Journal of Fluid Mechanics / Volume2 / Issue03 / May 1957, pp 237-262



Lecture  18 nov 2016:
- Saint Venant model, Shallow Water equations and KdV

download the file

Books for this chapters:
Linear and Nonlinear Waves Whitham
Lighthill
Nonlinear water waves, L. Debnath



Lecture 9 nov 2016 :
- Homogenization

download the file

Books for these chapters:
J. Kevorkian, J Cole, Perturbation methods in applied mathematics. Applied Mathematical Sciences, vol. 34, Springer-Verlag, Berlin and New York, 1981
Perturbation methods J. Hinch  Cambridge University Press, (1991)
J. Sanchez-Palencia Rend.Sem. Math . Univ Politech Torino Vol.440, 1 (1986)



Lecture
-Model Equations/ Model equations in Mechanics,

download the file




Exam :
-Exam

download the file of exam 09/10.
download the file of exam 10/11.
download the file of exam 11/12.
download the file of exam 12/13.
download the file of exam 13/14.
download the file of exam 14/15.
download the file of exam 15/16.
download the file of exam 16/17.
download the file of exam 17/18.




Conclusion :
- final notes on the method as conclusion.