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. ε "Asymptotic Analysis in Paris" up to date oct 2024 this page:  http://www.lmm.jussieu.fr/~lagree/COURS/M2MHP/index.html last year:  http://www.lmm.jussieu.fr/~lagree/COURS/M2MHP/index2024.html

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M2 MF2A P6 : Fluid Mechanics, M2 Fluid Mechanics : Sorbonne Université
MEC653 Multiscale hydrodynamic phenomena

first semester 2024-2025
- 1 week exam ( ?? ??? Dec.)
NSF01-Multiscale hydrodynamic phenomena : planningM2.MF2A
Web Page of MF2A : M2.MF2A

MU5MEF15 Multiscale hydrodynamic phenomena (P.Y Lagrée) Fri, 8:30am – 12:30pm Where 14-24 s 305

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C01 F 20 september      08h30  12h30
C02 F 27 september      08h30  12h30
C03 F 04 october      08h30  12h30
C04 F 11 october      08h30  12h30
C05 F 18 october      08h30  12h30
C06 F 25 octobrer      08h30  12h30
C00 F 01 november : Halloween, no lecture
C07 F 08 november      08h30  12h30
C08 F 15 november      08h30  12h30
C09 F ??? december exam 08h30  12h00

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Lecture:  20 sept 2024
- simple introduction in the free-fall case  
- definition of asymptotic developments  
- simple example of singular problem
- Friedrichs problem
- a non linear example with '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 (1991)
Perturbation methods Hinch chapter 5
Perturbation methods in fluid mechanics M. Van Dyke (1975)
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
Analyse asymptotique et couche limite; Méthodes Asymptotiques Mauss and Cousteix  (2000) Springer
Asymptotic analysis and boundary layers Mauss and Cousteix  (2007) Springer
Germain Paul , Fluid Dynamics, Les Houches 1973 (p 75-88)

Students of SU can obtain the ebook Nayfeh Nonlinear Oscillations

Web:
scholarpedia "Singular_Perturbation_Theory"
J. Hunter course (2004)

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Lecture 2,   27 09 2024
- Feyman averaging method/ Method of Averaging
- Multiple scale analysis
- WKB theory
- Example of the damped oscillator

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 J. Hinch  Cambridge University Press, (1991)
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
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  
Germain Paul , Fluid Dynamics, Les Houches 1973 (p 66-75)

Web:
scholarpedia
J. Hunter course (2004)

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Lecture not since 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
T. J. Pedley "The Fluid Mechanics of Large Blood Vessels", Appendix

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Lecture 3 : 10 oct 2024:
video 2.1

- 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 (p 18 et 19)

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lecture 4 : 17 octobre 2024
video 2.2 (captation October 9 2020)

video 3.1 (captation October 16 2020)

- Ideal Fluid
2.3 linearized Euler boundary conditions
2.4 linearized Euler incompressible flow
2.8 linearized Euler compressible supersonic flow
2.6 linearized Shallow water flow
video 3.2 (October 21 2022)

3.1 Blasius solution on a flat plate
3.4 Falkner Skan solution

download the file of lecture 3 and 4

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

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Lecture 5 : 20 october 2023
video 4.1 (October 22 20)
- Boundary Layer separation,
video 4.2 (October 22 20)
- Interactive Boundary Layer
video 4.3 (ctober 22 20)
G Jam (ctober 22 20)
- Triple Deck

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.

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Lecture  13 nov 2023
- Small Reynolds fluid dynamics, Oseen.

video 6.2 (20 nov 20)
Jam 6.2 (20 nov 20)
download the file of lecture X

Books for this chapter:
Perturbation methods in fluid mechanics M. Van Dyke chapter 8
Fluid Mechanics Academic Press, P.K. 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

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Lecture  6: 27 october 2023 and 10 nov:
- Saint Venant model, Shallow Water equations and KdV

video 5.1 (6 nov 20)
video 5.2 (6 nov 20)
Google Jam 5.1 (6 nov 20)
video 5.3 (6 nov 23)
Google Jam 5.2 (13 nov 20)
download the pdf file of the lecture (see as well file for shallow water and file).

video explaining slowly the "Euler Equation with free surface without dimension"
video explaining slowly how those equations in the shallow and small perturbation limit give the d'Alembert wave equation by linearisation.
video explaining briefly the link between "Euler Equation with free surface without dimension" and the potential description as described in the pdf file of the lecture.

Books for this chapter:
Linear and Nonlinear Waves Whitham, Wiley 1974. Students of SU can obtain the ebook Linear and Nonlinear Waves, Whitham
Waves in Fluids, Lighthill, Cambridge University Press, 1978
Nonlinear water waves, L. Debnath, Elsevier 1994

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Lecture 13 nov 2022:
- Homogenization

Google Jam (20 nov 20)
video 6.1 (20 nov 20)
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)

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Lecture
-Model Equations/ Model equations in Mechanics,

download the file

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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.
download the file of exam 20/21.
download the file of exam 21/22.
download the file of exam 22/23.
download the file of exam 23/24.
download the file of exam 24/25.

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