Effects of blood models on flows through a stenosis

“…represents volume; dS equals n · dS, where n is the unit vector normal to the surface dS; i x ; i y ; i z are the unit vectors in the x; y and z directions, respectively; p is the pressure and is the density. Following the analysis in Reference [19] the shear-stress tensor in the di usion terms is expressed in the case of non-Newtonian uids as…”

Section: Governing Equationsmentioning

confidence: 99%

Flow effects of blood constitutive equations in 3D models of vascular anomalies

Neofytou

Tsangaris

2005

Numerical Methods in Fluids

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SUMMARYThe e ects of di erent blood rheological models are investigated numerically utilizing two threedimensional (3D) models of vascular anomalies, namely a stenosis and an abdominal aortic aneurysm model. The employed CFD code incorporates the SIMPLE scheme in conjunction with the ÿnite-volume method with collocated arrangement of variables. The approximation of the convection terms is carried out using the QUICK di erencing scheme, whereas the code enables also multi-block computations, which are useful in order to cope with the two-block grid structure of the current computational domain. Three non-Newtonian models are employed, namely the Casson, Power-Law and Quemada models, which have been introduced in the past for modelling the rheological behaviour of blood and cover both the viscous as well as the two-phase character of blood. In view of the haemodynamical mechanisms related to abnormalities in the vascular network and the role of the wall shear stress in initiating and further developing of arterial diseases, the present study focuses on the 3D ow ÿeld and in particular on the distribution as well as on both low and high values of the wall shear stress in the vicinity of the anomaly. Finally, a comparison is made between the e ects of each rheological model on the aforementioned parameters. Results show marked di erences between simulating blood as Newtonian and non-Newtonian uid and furthermore the Power-Law model exhibits di erent behaviour in all cases compared to the other models whereas Quemada and Casson models exhibit similar behaviour in the case of the stenosis but di erent behaviour in the case of the aneurysm.

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“…U denotes an interface flux SMART [22] and MUSCL [23]. In the past years, Neofytou [24,25] used the SIMPLE method coupled with the QUICK scheme on collocated structured grids for generalized Newtonian fluid flows of Power-Law, Bingham, Quemada and Casson models. Miranda et al [26] employed the FVM in conjunction with SIMPLE on non-uniform structured grids for Newtonian and generalized Newtonian fluid flows in a planar T-junction.…”

Section: Introductionmentioning

confidence: 99%

A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

Gao

Ru-xun

2009

Acta Mech Sin

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This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow (Power-Law model). The collocated (i.e. non-staggered) arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.

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Effects of blood models on flows through a stenosis

Cited by 44 publications

References 27 publications

LES of non-Newtonian physiological blood flow in a model of arterial stenosis

LES of non-Newtonian physiological blood flow in a model of arterial stenosis

Flow effects of blood constitutive equations in 3D models of vascular anomalies

A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

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