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)

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.

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