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**A DF-IBM/NSCD coupling framework to simulate immersed particle interactions.**
*(English)*
Zbl 1439.74405

Summary: Immersed granular flows are present widely in different domains under different forms (at various scales) such as in nature (rivers, muds, atmosphere, blood…), and in many industrial applications (detergents, cosmetics, etc…). Studying such flows properly requires one to represent well the physics behind their dynamics: the fluid/solid interactions (FSI), the solid/solid interactions (SSI) and the coupling mechanisms at various scales.

In this work, a new coupling framework to simulate immersed granular flows has been developed. The FSI has been modeled using a direct-forcing immersed boundary method (DF-IBM) and implemented in the parallelized “PELICANS” C++ library. In this DF-IBM, all the mathematical equations, including the direct-forcing term, are discretized, both in space and time, and solved iteratively via a finite-volume and projection methods on Eulerian Grids. A sharp-edge interface, that can be smoothed, is used to represent the fluid/solid transition. The modeling of the multiple SSI at the grain’s scale is based on the Non-Smooth Contact Dynamics (NSCD) approach developed in the “LMGC90” open-source library. The coupling of the two softwares “PELICANS” and “LMGC90”, called Xper, provides an efficient framework to simulate and study dense immersed granular flows by taking into account, both advanced contact laws between grains, and hydrodynamic interactions. We address in this paper the effects of imposing a fluid-ring numerically (or fluid-mesh-cells) around two settling solid disks on modifying their dynamics. The DF-IBM approach implemented in Xper is validated, on a 2D flow over a stationary rigid cylinder benchmark, and on the settling of a rigid buoyant sphere in an incompressible laminar fluid at different Reynolds numbers. The numerical results are in good agreement with experimental and numerical data from the literature.

In this work, a new coupling framework to simulate immersed granular flows has been developed. The FSI has been modeled using a direct-forcing immersed boundary method (DF-IBM) and implemented in the parallelized “PELICANS” C++ library. In this DF-IBM, all the mathematical equations, including the direct-forcing term, are discretized, both in space and time, and solved iteratively via a finite-volume and projection methods on Eulerian Grids. A sharp-edge interface, that can be smoothed, is used to represent the fluid/solid transition. The modeling of the multiple SSI at the grain’s scale is based on the Non-Smooth Contact Dynamics (NSCD) approach developed in the “LMGC90” open-source library. The coupling of the two softwares “PELICANS” and “LMGC90”, called Xper, provides an efficient framework to simulate and study dense immersed granular flows by taking into account, both advanced contact laws between grains, and hydrodynamic interactions. We address in this paper the effects of imposing a fluid-ring numerically (or fluid-mesh-cells) around two settling solid disks on modifying their dynamics. The DF-IBM approach implemented in Xper is validated, on a 2D flow over a stationary rigid cylinder benchmark, and on the settling of a rigid buoyant sphere in an incompressible laminar fluid at different Reynolds numbers. The numerical results are in good agreement with experimental and numerical data from the literature.

### MSC:

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

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

74E20 | Granularity |

76T25 | Granular flows |

74-04 | Software, source code, etc. for problems pertaining to mechanics of deformable solids |

### Keywords:

immersed granular flows; fluid/structure interaction; direct-forcing; immersed boundary method; non-smooth contact dynamics
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\textit{T. Dbouk} et al., Comput. Methods Appl. Mech. Eng. 309, 610--624 (2016; Zbl 1439.74405)

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