Modélisation numérique 1

Dernière mise à jour le 26 avril 2024

Présentation

This course introduces the basic numerical methods used to solve fluid mechanics problems (finite differences, spatial discretization, integration in time, accuracy, order, convergence, stability). The course is taught in English. Practicing is an essential part of the course. The programming language is Python.

Pré-requis nécessaires

Pre-requisites

Linear algebra, ordinary differential equations

Objectifs

Objectives

Acquire the fundation concepts of numerical modelling. Be able to implement numerical methods in Python. Be able to test and validate a numerical code.

Compétences visées

Abilities provided

Identify numerical methods for problem solving and validate results ; know and know how to use numerical simulation codes to tackle complex problems

Descriptif

Contents

Classes are done in computer rooms, they blend theory and practice with a computer. Small homework are asked from one class to another. The final mark is composed of a final exam (50 % of the mark), in computer room, and of two personal projects (25% each). The course is split in two parts

Part 1: Spatial discretization

finite vs volume methods
staggered grid
boundary conditions
matrix representation
eigenvectors and eigenvalues
iterative methods to solve system of equations

Part 2: Integration of ordinary differential equations

order, convergence, stability
explicit vs implicit schemes
Runga Kutta methods
multi-stages methods