# Coupled simulation for thin shells

### Standard Euler equations with shock wave - Timings

- Average pressure of 1D simulation prescribed by a pure shock wave solution of non-reactive Euler equations with shock speed chosen to
equal detonation velocity
- Coupled simulation: AMR base mesh 40x40x80, 2 additional levels with refinement factor 2, ~3,000,000 cells. Modeled tube thickness
0.17 cm, (2x thicker than in experiment). Solid Mesh: ~ 5,000 elements.
- Calculation run on ALC (26 fluid CPUs, 6 solid CPUs): ~4.54 h real time
- Performance: fractions of time spent in different parts of fluid AMR solver

Task | % |

Fluid dynamics | 31.3 |

Boundary setting | 22.3 |

Interpolation | 5.9 |

Recomposition | 6.8 |

GFM Extra-/Interpolation | 10.9 |

Locating GFM cells | 5.5 |

GFM Various | 3.0 |

Receive shell data | 4.3 |

Closest point transform | 2.6 |

Node velocity assignment | 2.2 |

Construct nodal pressure | 1.5 |

Misc | 3.7 |

### Reactive Euler equations with full Hydrogen-Oxygen reaction mechanism

- 9 termally perfect species, 34 elementary reactions from Westbrook-Mechanism, see NumSimGasDet for mechanism
- Coupled simulation: AMR base mesh 20x20x160, 2 additional levels with refinement factor 2, ~1,100,000 cells. Modeled tube thickness
0.15 cm, (2x thicker than in experiment). Solid Mesh: ~ 5,000 elements.
- Simulated time 0.002 sec
- Hydrogen and oxygen are premixed with argon in molar ratios 2:1:7 in the entire tube, initial temperature 298 K, pressure 30 kPa
- A relatively weak shock wave propagates through the tube (T=624K, u=-478.5m, p=160kPa).
- After reflection at the
*now closed* end the temperature in the regions overrun by the reflected shock is >1100K.
- A detonation wave will be initiated at the closed end. It was verified with 1D simulations that the actual mesh can support this detonation roughly. It will arise by the time when the reflected shock will be in the middle of the tube again around t=0.0015 sec, which is by the time when the movie below ends.
- Simulation to t=0.0015 run on 58 CPUs fluid, 10 CPUs solid ALC: approx. 1600h CPU.

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