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| Name | Last modified | Size | Description |
|---|---|---|---|---|
| Parent Directory | - | ||
| edp/ | 2019-09-23 14:28 | - | |
| old/ | 2022-11-02 19:04 | - | |
| w1/ | 2019-09-23 14:24 | - | |
| w2/ | 2020-02-14 13:18 | - | |
| w3/ | 2019-10-07 12:34 | - | |
| w4/ | 2019-10-14 15:20 | - | |
| w5/ | 2020-06-18 15:12 | - | |
| Stokes-bug.edp | 2017-10-23 09:32 | 582 | |
| NSFallingEllipse.edp | 2020-06-18 15:41 | 4.4K | |
| README-2018-19.html | 2018-10-18 10:46 | 11K | |
| README.html | 2019-10-22 16:42 | 15K | |
| Projet2018.tex | 2018-10-01 07:27 | 21K | |
| BC-STOKES.pdf | 2016-10-24 09:05 | 160K | |
| Convect.pdf | 2017-05-10 12:26 | 190K | |
| Projet2018.pdf | 2018-10-01 07:28 | 241K | |
| NS3book.pdf | 2017-05-10 12:26 | 1.4M | |
| Cours-FFv4.pdf | 2019-09-23 10:57 | 2.5M | |
| FreeFEM-documentation.pdf | 2019-09-23 13:59 | 34M | |
Cours Numerical methods for fluid mechanics (5AF03 )
F. HECHT & S. ZALESKI
UPMC / Master II Fluid Mechanics / SPI
Version 21 Oct.. 2019 F. Hecht part.
Université Pierre et Marie Curie
F. Hecht, (Class Room 24-34 310)
F. HECHT (Cours)
Monday room: 24.34.310 8h30 – 12h30 is the , Planning
Modelling, Mathematical Analysis and Scientific Calculation in Household Waste Management Cours CIMPA, Kénitra 2019 G 03-13Juilet 2019 le fichier archive des presentations, exemples et le dossier .
Week 1) 23 Sep 2019
Presentation of Heat equation.
Writing the weak form or the variational form
Presentation of the finite element and how tho build a finite element space.
Presentation of FreeFem++
First solve the stationary Heat equation with all kind of boundary condition (B.C)
Dirichlet, Neumann,
Verified the classical error of Finite element.
The freefem++ example is in directory of w1/
To do
1) install freefem++ precompile from the web site http://www.freefem.org/ff++/ for mac or windows systems
and for linux compile le version using http://www.freefem.org/ff++/linux.php (with ./configure --enable_download
to have a full version of freefem++, the mpi version is not mandatory).
2) launch FreeFem++ on fish.edp example on you computer.
3) try do add the computation of the potenteil field in file w1/Potentiel-flow-NACA12.edp
Week 2) 30 sept 2019
explication of the regularization to full Neuman Boundary condition.
The computation of irrotational flow with Joukowski condition.
see section 2. 2 of NS3book.pdf
the full solution is in w2/irrot-low-adap.edp
Week 3) 6 october
Variational formulation of Stokes Problem.
Approximation of the Stationnary Stokes problem
Problem of compatibility on discretization on Velocity and Pressure.
see example w3/Stokes-v0.edp
Boundary condition problem of compatibility ( zero output flux)
a discrete level see w3/Stokes-bug.edp
a first way to do no linear problem (fixe point loop) w3/Navier-Stokes.edp
for more information of boundary condition for Stokes problem see BC-STOKES.pdf
Week 4) 14 october
Newton algorithm to speed up the convergence
page 153 of Cours-FFv4.pdf
Computation of derivative of operator.
Example on Minimal surface problem. with fixe point algorithme
is directory s4, they are example of steady state problem of Navier-Stokes , Rayleigh-Bernard flow
Home Work for next week, Implement the newton method of the minimal surface problem
after few iteration of fixed point method in s4/MinSurf.edp. And Change the func g ,
func g= sin(3*atan2(y,x));
in
func g= sin(10*atan2(y,x));
the err test : the err test if(err < 1e-7) break;
...
try to optimize the speed of resolution ..
Week 5) 21 october
Introduction of time scheme
Euler explicite (Warning the stability condition dt/h^2 < Cte for elliptique equation)
Euler implicite (alway stable)
The theta-schema (alway stable if theta > 0.5)
BDF schema for higher order see Backward differentiation formula - Wikipedia, the free encyclopedia