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**Oberlack, Martin and Cheviakov, Alexei F.** (2010):

*Higher-order symmetries and conservation laws of the G-equation for premixed combustion and resulting numerical schemes.*

In: Journal of Engineering Mathematics, 66 (1), Springer, pp. 121-140, ISSN 0022-0833,

[Online-Edition: http://dx.doi.org/10.1007/s10665-009-9339-2],

[Article]

## Abstract

It is shown that the set of computable local symmetries of the G-equation for flame-front propagation of premixed combustion is considerably extended if higher-order symmetries are considered. Classical point symmetries are exhaustively discussed by Oberlack et al. (Combust Theor Model 5:363–383, 2001). Further, if the flow velocity is zero, an infinite series of higher-order symmetries has been derived by Oberlack (J Calcutta Math Soc 1:41–52, 2004). Presently it is evidenced that the G-equation also admits an infinite number of higher-order symmetries for an arbitrary velocity field. Higher-order symmetries involving derivatives up to second order are computed. Geometrical and kinematic interpretations of the symmetries are given. For the special case of constant flow velocity, an infinite set of local conservation laws of the G-equation has been derived using the direct method. It is demonstrated how the derived infinite sets of local symmetries and conservation laws can be used to develop novel numerical schemes (including higher-order ones) to perform computations in practical applications involving the G-equation.

Item Type: | Article |
---|---|

Erschienen: | 2010 |

Creators: | Oberlack, Martin and Cheviakov, Alexei F. |

Title: | Higher-order symmetries and conservation laws of the G-equation for premixed combustion and resulting numerical schemes |

Language: | English |

Abstract: | It is shown that the set of computable local symmetries of the G-equation for flame-front propagation of premixed combustion is considerably extended if higher-order symmetries are considered. Classical point symmetries are exhaustively discussed by Oberlack et al. (Combust Theor Model 5:363–383, 2001). Further, if the flow velocity is zero, an infinite series of higher-order symmetries has been derived by Oberlack (J Calcutta Math Soc 1:41–52, 2004). Presently it is evidenced that the G-equation also admits an infinite number of higher-order symmetries for an arbitrary velocity field. Higher-order symmetries involving derivatives up to second order are computed. Geometrical and kinematic interpretations of the symmetries are given. For the special case of constant flow velocity, an infinite set of local conservation laws of the G-equation has been derived using the direct method. It is demonstrated how the derived infinite sets of local symmetries and conservation laws can be used to develop novel numerical schemes (including higher-order ones) to perform computations in practical applications involving the G-equation. |

Journal or Publication Title: | Journal of Engineering Mathematics |

Volume: | 66 |

Number: | 1 |

Publisher: | Springer |

Uncontrolled Keywords: | Conservation law; G-equation; Level-set equation; Premixed combustion; Symmetry |

Divisions: | 16 Department of Mechanical Engineering 16 Department of Mechanical Engineering > Fluid Dynamics (fdy) Exzellenzinitiative Exzellenzinitiative > Clusters of Excellence Zentrale Einrichtungen Exzellenzinitiative > Clusters of Excellence > Center of Smart Interfaces (CSI) |

Date Deposited: | 24 Aug 2011 18:14 |

Official URL: | http://dx.doi.org/10.1007/s10665-009-9339-2 |

Additional Information: | dio:10.1007/s10665-009-9339-2 |

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