##
**Computational methods for parachute fluid-structure interactions.**
*(English)*
Zbl 1354.76113

Summary: The computational challenges posed by fluid-structure interaction (FSI) modeling of parachutes include the lightness of the parachute canopy compared to the air masses involved in the parachute dynamics, in the case of “ringsail” parachutes the geometric complexities created by the construction of the canopy from “rings” and “sails” with hundreds of ring “gaps” and sail “slits”, and in the case of parachute clusters the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling (T\(\star\)AFSM) has successfully addressed these computational challenges with the Stabilized Space-Time FSI (SSTFSI) technique, which was developed and improved over the years by the T\(\star\)AFSM and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI technique. The quasi-direct and direct coupling techniques developed by the T\(\star\)AFSM, which are applicable to cases with incompatible fluid and structure meshes at the interface, yield more robust algorithms for FSI computations where the structure is light and therefore more sensitive to the variations in the fluid dynamics forces. The special technique used in dealing with the geometric complexities of the rings and sails is the Homogenized Modeling of Geometric Porosity, which was developed and improved in recent years by the T\(\star\)AFSM. The Surface-Edge-Node Contact Tracking (SENCT) technique was introduced by the T\(\star\)AFSM as a contact algorithm where the objective is to prevent the structural surfaces from coming closer than a minimum distance in an FSI computation. The recently-introduced conservative version of the SENCT technique is more robust and is now an essential technology in the parachute cluster computations carried out by the T\(\star\)AFSM. We provide an overview of the core and special techniques developed by the T\(\star\)AFSM, present single-parachute FSI computations carried out for design-parameter studies, and report FSI computation and dynamical analysis of two-parachute clusters.

### MSC:

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

74S05 | Finite element methods applied to problems in solid mechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

76G25 | General aerodynamics and subsonic flows |

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\textit{K. Takizawa} and \textit{T. E. Tezduyar}, Arch. Comput. Methods Eng. 19, No. 1, 125--169 (2012; Zbl 1354.76113)

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[110] | Tezduyar, TE; Senga, M; Vicker, D, Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ\(β\) shock-capturing, Comput Mech, 38, 469-481, (2006) · Zbl 1176.76077 |

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[130] | Johnson, AA; Tezduyar, TE, 3D simulation of fluid-particle interactions with the number of particles reaching 100, Comput Methods Appl Mech Eng, 145, 301-321, (1997) · Zbl 0893.76043 |

[131] | Tezduyar, TE, CFD methods for three-dimensional computation of complex flow problems, J Wind Eng Ind Aerodyn, 81, 97-116, (1999) |

[132] | Tezduyar, T; Osawa, Y, Methods for parallel computation of complex flow problems, Parallel Comput, 25, 2039-2066, (1999) |

[133] | Hoerner SF (1993) Fluid dynamic drag. Hoerner Fluid Dynamics, Bakersfield |

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