Course Syllabus 2014/2015

Module : AN200

Title :

Level :

Document(s) :

Title :

Numerical approximation and industrial problems I

Number of hours : Lecture : 18.00 h

Tutorial classes : 25.33 h

Individual work : 22.00 h

ECTS credits : Tutorial classes : 25.33 h

Individual work : 22.00 h

4.00

Evaluation : S1: ET(2h,E,sd,sc) x1 Detail of the nomenclature used for the creation of the evaluation code

Teacher(s) : AREGBA Denise

MIEUSSENS Luc - Responsible

MAIRE Pierre-Henri

Shared by UV(s) : MIEUSSENS Luc - Responsible

MAIRE Pierre-Henri

Level :

second year module

Abstract :
The goal of this course is to show some fundamental
elements of numerical approximation of partial difference
equations. It will be restricted to linear problems, like diffusion
and convection, since these phenomenons can be observed in most of
mechanical problems. Most of the course will be devoted to the method
of finite differences for one dimensional problems. Main notions like
accuracy, stability, convergence, numerical diffusion and dispersion,
will analyzed. The last part of the course will be an introduction to
the finite volume methods, which is well suited to multidimensional
problems, in particular for conservation laws of fluid mechanics.
Finite Difference Methods for Ordinary and Partial Differential
Equations, Steady State and Time Dependent Problems, Randall
J. LeVeque, SIAM, 2007
Finite Volume Methods for Hyperbolic Problems, Randall J. LeVeque, Cambridge University Press, 2002.

Plan : The course is based on two books:

The numerical methods presented in the course will be studied with exercices and programming sessions.

- PDEs in Mechanics
- Approximation of derivatives with finite differences
- A boundary value problem: the heat equation
- Numerical approximation of the unsteady heat equation by finite differences
- Numerical approximation of the unsteady convection equation by finite differences
- Finite volume method for multidimensional convection problems

- Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems, Randall J. LeVeque, SIAM, 2007
- Finite Volume Methods for Hyperbolic Problems, Randall J. LeVeque, Cambridge University Press, 2002.