The ghost fluid method for deflagration and detonation discontinuities.

*(English)*Zbl 0955.76071Summary: The level set method for multiphase compressible flows is simple to implement, especially in the presence of topological changes. However, this method was shown to suffer from large spurious oscillations. A new ghost fluid method (GFM) was developed to remove these spurious oscillations by minimizing the numerical smearing in the entropy field with the help of an isobaric fix technique. The GFM was designed for traditional contact discontinuities where the interface moves with the fluid velocity only. In this paper, the GFM is extended to treat multimaterial interfaces where the interface velocity includes a regression rate due to the presence of chemical reactions converting one material into another. Specifically, we consider interface models for deflagration and detonation discontinuities. The resulting numerical method is robust and easy to implement.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76N15 | Gas dynamics (general theory) |

76T30 | Three or more component flows |

76V05 | Reaction effects in flows |

##### Keywords:

level set method; multiphase compressible flows; ghost fluid method; multimaterial interfaces; chemical reactions; deflagration; detonation
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\textit{R. P. Fedkiw} et al., J. Comput. Phys. 154, No. 2, 393--427 (1999; Zbl 0955.76071)

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