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

Multiscale Hydrodynamic Phenomena:

Method of Matched Asymptotic Expansions,
Multiple Scale Analysis, Boundary Layers, Triple Deck. Homogenisation.

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"Asymptotic Analysis in Paris"




up to date 14 nov 2019
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 2019-2020
- 1 week free
- 1 week exam (Friday XXth Dec.)
NSF01-Multiscale hydrodynamic phenomena
planningM2.MF2A


planningM2.MF2A

MU5MEF15 - SU (5AF01-MEC 653) Multiscale hydrodynamic phenomena (P.Y Lagrée) Fri, September 27, 8:30am – 12:30pm Where Salle: 56.66.112c


C01 F 27 september      08h30  12h30
C03 F 04 october      08h30  12h30
C04 F 11 october      08h30  12h30
C05 F 18 october      08h30  12h30
C00 F 25 october      FREE
C00 F 01 november      Halloween
C06 F 08 november      08h30  12h30
C07 W 13 november      08h30  12h30
C08 F 15 november      08h30  12h30
C09 F 22 november      08h30  12h30
Dec F 04 december exam 08h30  12h00



Lecture:  27 sept 2019
- simple introduction in the free-fall case  
- definition of asymptotic developments  
- simple example of singular problem
- Friedrich problem
- a non linear example: shocks and boundary layers

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

Students of SU can obtain the ebook Nayfeh Nonlinear Oscillations

Web:
scholarpedia
Hunter course




 
Lecture 2,   11 oct 2019
- 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)
Fluid Dynamics, Part 2 Asymptotic Problems of Fluid Dynamics Anatoly I. Ruban (2015)
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  : 18 oct 2019:
- Self similar solutions

only heat equation in 2019
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
Germain Paul , Fluid Dynamics, Les Houches 1973


Lecture 3 : 18 oct 2019
- Ideal Fluid
2.3 linearized Euler boundary conditions
2.4 linearized Euler incompressible flow
2.8 linearized Euler compressible supersonic flow
et 3.1 Blasius solution on a flat plate

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
Fluid Dynamics, Part 3 Boundary Layers Anatoly I. Ruban (2017)
Fluid Dynamics, Part 2 Asymptotic Problems of Fluid Dynamics Anatoly I. Ruban (2015)
Cousteix Books; Mauss Cousteix Books
Boundary Layer Theory Schlichting and Gersten



Lecture : 2nov 2019
- Boundary Layer separation, Triple Deck
- Interactive Boundary Layer

download the file on triple deck and the file on IBL
slides
Books for this chapter:
SteinruckAsymptotic Methods in Fluid Mechanics: Survey and Recent Advances
Schlichting Gersten and Schlichting Boundary Layer Theory
Fluid Dynamics, Part 3 Boundary Layers Anatoly I. Ruban (2017)
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  13 nov 2019
- 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 chapter:
Linear and Nonlinear Waves Whitham
Students of SU can obtain the ebook Linear and Nonlinear Waves, Whitham
Waves in Fluids, Lighthill
Nonlinear water waves, L. Debnath



Lecture 13 nov 2019 :
- 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)

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.
download the file of exam 18/19.
download the file of exam 19/20.




Conclusion :
- final notes on the method as conclusion of "Asymptotics in Paris".