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Comparison of some Lie-symmetry-based integrators

M. Chhay 1 Emma Hoarau 2 A. Hamdouni 3 P. Sagaut 4
1 LOCIE - Laboratoire Optimisation de la Conception et Ingénierie de l'Environnement
2 ONERA - The French Aerospace Lab [Châtillon]
3 GSMA - Groupe de spectrométrie moléculaire et atmosphérique
4 DALEMBERT - Institut Jean le Rond d'Alembert
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.
Keywords : Invariant scheme Symmetry Lie group method Discrete differential invariant Moving frame
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Journal articles
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Submitted on : Wednesday, April 6, 2016 - 6:08:21 PM
Last modification on : Tuesday, December 14, 2021 - 3:04:26 AM

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CNRS | UPMC | IJLRDA | UNIV-SAVOIE | ONERA | URCA | GSMA | SORBONNE-UNIVERSITE | SU-SCIENCES | LOCIE | UGA | INES

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M. Chhay, Emma Hoarau, A. Hamdouni, P. Sagaut. Comparison of some Lie-symmetry-based integrators. Journal of Computational Physics, Elsevier, 2011, 230 (5), pp.2174-2188. ⟨10.1016/j.jcp.2010.12.015⟩. ⟨hal-01298900⟩

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