A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics.

*(English)*Zbl 1244.76073Summary: The current paper reports on the development and validation of a localized collocation meshless method (LCMM) to model laminar incompressible flows. A high order upwinding scheme was devised to dampen the numerical oscillations arising in convection-dominated flows. Subsequently, the LCMM was analytically validated and demonstrated to yield third-order accurate solutions when compared to a benchmark analytical decaying vortex solution. Numerical validations are provided by comparison with the finite volume commercial (FVM) solver Fluent 6.2. The flow geometry for the numerical validation arises from a biomedical application that consists of modeling blood flow in the inter-connection between a bypass graft and an artery. Very good agreement was found between the LCMM and the FVM.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76Z05 | Physiological flows |

92C35 | Physiological flow |

##### Software:

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\textit{Z. El Zahab} et al., Eng. Anal. Bound. Elem. 33, No. 8--9, 1045--1061 (2009; Zbl 1244.76073)

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