Numerical methods for interface coupling of compressible and almost incompressible media.

*(English)*Zbl 1459.65214The authors develop computational simulations of the shock wave passing from gas into a thin elastic solid and into a nearly incompressible fluid. It is shown that if the solid interface is very thin, it can be neglected. The model uses Euler equations for compressible fluids coupled with a Tammann equation of state to model both compressible gas and almost incompressible materials. A three-dimensional axisymmetric model of these equations is solved using high-resolution shock-capturing methods, with newly developed Riemann solvers and limiters. The methods are extended to use a mapped grid to allow more complicated interface geometry and they can be adapted to work with adaptive mesh refinement for higher resolution and faster computations. The Clawpack software is used to implement the method.

Reviewer: Abdallah Bradji (Annaba)

##### MSC:

65N08 | Finite volume methods for boundary value problems involving PDEs |

65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |

65Z05 | Applications to the sciences |

76N15 | Gas dynamics (general theory) |

35Q31 | Euler equations |

92C50 | Medical applications (general) |

76L05 | Shock waves and blast waves in fluid mechanics |

##### Keywords:

Euler equations; tammann equation of state; compressible and almost incompressible fluid interfaces; finite volume methods; mapped grids; shock tube; traumatic brain injury
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\textit{M. J. Del Razo} and \textit{R. J. LeVeque}, SIAM J. Sci. Comput. 39, No. 3, B486--B507 (2017; Zbl 1459.65214)

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