Cours Numerical methods for fluid mechanics (5AF03 )
F. HECHT & S. ZALESKI
UPMC / Master II Fluid Mechanics / SPI
Version 15 Oct.. 2018 F. Hecht part.
Université Pierre et Marie Curie
F. Hecht, (Class Room 14.24.205)
F. HECHT (Cours)
Monday room: 24.34.310 8h30 – 12h30 is the , Planning
A cours of FreeFem++ : An Introduction to Scientific Computing using Free Software FreeFem++ , August 28 to September 1 2017, Department of Mathematics, University of Pittsburgh, USA the zip file of the folder (presentation, examples, 7.8Mb) and the folder .
Week 1) 1 October 2018
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 FreFem++
First solve the stationary Heat equation with all kind of boundary condition (B.C)
Verified the classical error of Finite element.
The freefem++ example is in directory of w1/
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.
Week 2) 8 October 2018
The computation of irrotational flow with Joukowski condition.
see section 2. 2 of NS3book.pdf
Introduction of time scheme
Euler explicite (Warning the stabling condition dt/h^2 < Cte for elliptque 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
Week 3) 15 October 2018
Non Linear Problem
Fixe point algorithme, Newton's algortitme
Approximation of the Stationnary Stokes problem
incompressible ( boundary condition) Navier-Stokes