Non-Newtonian flow in branched pipes and artery models.

*(English)*Zbl 1198.76163Summary: This work concerns finite element analysis for a class of generalized Newtonian flows through branching pipe or tube junctions in industrial applications or blood flow through arterial branches, prosthetic tube implants or in biomedical engineering devices. A two-step morphing transformation is developed and implemented to map a generic coplanar 3D branching flow configuration to general out-of-plane deformed geometry including local constriction/dilation ‘defects’ suitable for modeling specific arterial flow and industrial flow applications. Unstructured 3D meshes may be generated in the reference configuration and morphed to the application configuration. The resulting meshes may be tangled and exhibit mesh quality degradation. Algorithms integrating mesh generation, morphing, untangling and cell shape control strategies are presented.

Phenomenological studies are conducted with the Powell-Eyring class as a representative model to determine local details of shear-thinning flow behavior as well as the nature and location of high shear stress regions on artery branch walls. The supporting simulations are carried out using a parallel finite element scheme with domain decomposition by a sectional partitioning that takes advantage of the medial curve shape and specialized ILU preconditioning.

Phenomenological studies are conducted with the Powell-Eyring class as a representative model to determine local details of shear-thinning flow behavior as well as the nature and location of high shear stress regions on artery branch walls. The supporting simulations are carried out using a parallel finite element scheme with domain decomposition by a sectional partitioning that takes advantage of the medial curve shape and specialized ILU preconditioning.

##### MSC:

76Z05 | Physiological flows |

76A05 | Non-Newtonian fluids |

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

92C35 | Physiological flow |

##### Keywords:

finite element method; two-step morphing transformation; Powell-Eyring model; ILU preconditioning
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\textit{W. L. Barth} et al., Int. J. Numer. Methods Fluids 57, No. 5, 531--553 (2008; Zbl 1198.76163)

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