# American Institute of Mathematical Sciences

2007, 2007(Special): 495-505. doi: 10.3934/proc.2007.2007.495

## Lie group study of finite difference schemes

 1 Onera, Computational Fluid Dynamics and Aeroacoustics Department (DSNA), BP 72, 20 avenue de la Division Leclerc, 92322 Châtillon Cedex, France 2 Université Pierre et Marie Curie-Paris 6, Institut Jean Le Rond d'Alembert, UMR CNRS 71900, Boîte courrier $n^0$ 162, 4 place Jussieu, 75252 Paris, cedex 05. France 3 ONERA, Computational Fluid Dynamics and Aeroacoustics Department (DSNA), BP 72, 20 avenue de la Division Leclerc, 92322 Châtillon Cedex, France

Received  September 2006 Revised  August 2007 Published  September 2007

Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference approximation, and lead to inaccurate numerical results. This paper deals with the analysis of symmetry group of finite difference equations, which is based on the differential approximation. We develop a new scheme, the related differential approximation of which is invariant under the symmetries of the original differential equations. A comparison of numerical performance of this scheme, with standard ones and a higher order one has been realized for the Burgers equation.
Citation: Emma Hoarau, Claire david@lmm.jussieu.fr David, Pierre Sagaut, Thiên-Hiêp Lê. Lie group study of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 495-505. doi: 10.3934/proc.2007.2007.495
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