Course Syllabus 2014/2015
 
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Module : AN200
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 :
4.00
Evaluation :
Teacher(s) :
AREGBA Denise
MIEUSSENS Luc - Responsible
MAIRE Pierre-Henri
Shared by UV(s) :
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.

The course is based on two books:

  • 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.

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

  • Plan :
      • 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
    Document(s) :
      • 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.