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**Adaptive \(h\)-refinement of 3D unstructured grids for transient problems.**
*(English)*
Zbl 0753.76099

Summary: An adaptive finite element scheme for transient problems is presented. The classic \(h\)-enrichment/ coarsening is employed in conjunction with a tetrahedral finite element discretization in three dimensions. A mesh change is performed every \(n\) time steps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved by pre- sorting the elements and then performing the refinement/coarsening groupwise according to the case at hand. Further reductions in CPU requirements are realized by optimizing the identification and sorting of elements for refinement and deletion. The developed technology has been used extensively for shock-shock and shock-object interaction runs in a production mode. A typical example of this class of problems is given.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

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

65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |

### Keywords:

compressible flow; \(h\)-enrichment/coarsening; tetrahedral finite element; protective layers; vectorizability; shock-object interaction
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\textit{R. Löhner} and \textit{J. D. Baum}, Int. J. Numer. Methods Fluids 14, No. 12, 1407--1419 (1992; Zbl 0753.76099)

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### References:

[1] | , and , ’Finite element methods for high speed flows’, AlAA-85-1531-CP, 1985. |

[2] | , and , ’Finite element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equations’, ICASE Rep. 87-4, 1987; |

[3] | Int. j. numer. methods fluids 7 pp 1093– (1987) |

[4] | Löhner, Commun. Appl. Numer. Methods 4 pp 717– (1988) |

[5] | Löhner, Comput. Methods Appl Mech. Eng. 61 pp 323– (1987) |

[6] | and , ’Numerical simulation of shock-elevated box interaction using an adaptive finite element shock capturing scheme’, AIAA-89-0653, 1989. |

[7] | and , ’Numetical simulation of shock interaction with complex geometry canisters’, in (ed.), Current Topics in Shock Waves. American Institute of Physics, New York, 1989. |

[8] | Oden, Comput. Methods Appl. Mech. Eng. 59 pp 327– (1986) |

[9] | Berger, J. Comput. Phys. 53 pp 484– (1984) |

[10] | , and , ’Adaptive mesh refinement on moving quadrilateral grids’, AIAA-89-1979-CP, 1989. |

[11] | and , ’Spatio-temporal adaptation algorithm for two-dimensional reacting flows’, AIAA-88-0510, 1988. |

[12] | Peraire, J. Comput. Phys. 72 pp 449– (1987) |

[13] | , , and , ’Finite element Euler computations in three dimensions’, AIAA-88-0032, 1988. · Zbl 0665.76073 |

[14] | Hner, Comput. Methods Appl. Mech. Eng. 75 pp 195– (1989) |

[15] | Löhner, Comput. Syst. Eng. 1 pp 257– (1990) |

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