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**Propagation of a strong discontinuity in a binary mixture of gases.**
*(English)*
Zbl 1499.35412

Summary: Strong discontinuities – shock-waves – arise in a continuous media under dynamic external loads. Simulation of their propagation in mixtures must take into account, for each mixture component, the mass, momentum, and energy conservation laws relating states of matter before and behind the shock front. This effort calculates the process of shock-wave propagation in a plane layer, i.e. a homogeneous mixture of two gases having different density. For this purpose, conservation laws, as well as quantities responsible for components interaction were numerically implemented. The Lagrangian stage of the Lagrangian-Eulerian calculations used the shock-wave computation method based on the solution of the system of nonlinear algebraic equations. Sensitivity of flow parameters to the cluster and pairwise interactions is investigated. Cluster interaction was shown to be the major contributor to velocities relaxation behind the strong discontinuity front. Profiles of thermodynamic quantities and mass velocities were obtained for each component.

### MSC:

35L67 | Shocks and singularities for hyperbolic equations |

39A10 | Additive difference equations |

76T99 | Multiphase and multicomponent flows |

### Keywords:

multicomponent media; conservation laws; shock wave; Lagrangian-Eulerian scheme; cluster interaction
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\textit{A. V. Krasilnikov} and \textit{V. F. Kuropatenko}, J. Comput. Eng. Math. 5, No. 3, 49--60 (2018; Zbl 1499.35412)

### References:

[1] | V. F. Kuropatenko, “New Models of Continuum Mechanics”, Journal of Engineering Physics and Thermophysics, 84:1 (2011), 77-99 |

[2] | Yu. M. Kovalev, V. F. Kuropatenko, “Analiz invariantnosti otnositelno preobrazovaniya Galileya nekotorykh matematicheskikh modelei mnogokomponentnykh sred”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 13, 69-73 · Zbl 1413.76051 |

[3] | V. F. Kuropatenko, E. S. Shestakovskaya, Osnovy chislennykh metodov mekhaniki sploshnoi sredy, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2017 |

[4] | V. F. Kuropatenko, “Ob odnom metode skvoznogo scheta udarnykh voln”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:1 (2014), 62-75 · Zbl 1290.76056 |

[5] | V. F. Kuropatenko, Modeli mekhaniki sploshnykh sred, Chelyab. gos. un-t, Chelyabinsk, 2007 |

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