Micro–macro simulations of a shear-thinning viscoelastic kinetic model: applications to blood flow

Abstract

This article is concerned with the numerical simulation of the flow of blood in small channels. Under certain flow conditions, blood is expected to behave like a viscoelastic fluid. Therefore a non-Newtonian, viscoelastic and shear-thinning finitely extensible non-linear elastic (FENE) dumbbell suspension model is used. The FENE dumbbell model is a coarse-grained molecular model that was developed for polymer solutions. The FENE model in this paper uses the variance reduction techniques of Brownian configuration fields and equilibrium control variates. The model has been implemented into a spectral element algorithm, which solves the stochastic differential equation together with the momentum and continuity equations. The temporal discretization of the convective term in the momentum equation is performed using a first-order time-splitting technique. An Euler–Maruyama predictor–corrector scheme has been used for the temporal discretization of the stochastic differential equation for the evolution of the configuration fields. Spatial discretization is performed using spectral element techniques, and the system of discretized equations is solved using a preconditioned conjugate gradient method. Results are presented for the start-up of Poiseuille flow in a planar channel, and for simulations of blood flowing through a small channel with a symmetric and a non-symmetric stenosis. The influence of the model parameters on the solution is described.

Keywords:

• FENE model
• viscoelastic fluid
• shear-thinning fluid
• blood flow
• stenosis
• spectral elements

AMS Subject Classifications::

• 76A05
• 76M22
• 65C30
• 92C50

Acknowledgement

This work has been partially supported by the project PTDC/MAT/68166/2006 and by CEMAT/IST through FCT's Funding Program.