Introduction

This project is part of the Hydrodynamic Instabilities course of O. Thual.

The purpose of this study is to understand the characteristics of Burgers
equation in 1D. The non linearity and the shock formation are the main
difficulty for correct solving. For the numerical computation the scheme
should be accurate enough to be able to render the strong gradients over
a limited set of points.

The work is dived is four parts:

- First the Presentation of Burgers’s equation gives some background information and gives an insight on expected results.
- In the Algorithm part, the FORTRAN 90 code used for numerical computation is given as well as the description of the various parameters that can be set.
- Scheme and Shock regroups the main part of the results studying the response of the different schemes, and the relation between shock formation and viscosity.
- Stability is a small part devoted to the stability of Burgers’s equation when additional terms are set.

The Author

Laurent Nack, 3rd Year CFD Student at ENSEEIHT.