Comparison of some Lie-symmetry-based integrators

Authors:
M. Chhay;E. Hoarau;A. Hamdouni;P. Sagaut
Affiliations:
LEPTIAB, Université de La Rochelle, Avenue Michel Crepeau, France;Institut Jean Le Rond d'Alembert, UMR 7190, Université Pierre et Marie Curie, 4 Place Jussieu - Case 162, F-75252 Paris cedex 5, France;LEPTIAB, Université de La Rochelle, Avenue Michel Crepeau, France;Institut Jean Le Rond d'Alembert, UMR 7190, Université Pierre et Marie Curie, 4 Place Jussieu - Case 162, F-75252 Paris cedex 5, France
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

Lie-symmetry based integrators are constructed in order to preserve the local invariance properties of the equations. The geometrical methods leading to discretized equations for numerical computations involve many different concepts. Therefore they give rise to numerical schemes that vary in the accuracy, in the computational cost and in the implementation. In this paper a comparison is made between some alternative Lie-symmetry based methods illustrated on the example of the Burgers equation. The importance of the symmetry preservation is numerically highlighted.