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A streamline upwind Petrov-Galerkin approach is also adopted in the discretization of the constitutive equation and the microstructure evolution equation. The numerical results presented begin with validation of our finite element scheme in a coaxial rheometer both for a prescribed homogeneous velocity field and for a fully two-dimensional calculation including the solution of the linear momentum equation. The consideration of blood flow in a straight channel allows us to test convergence of our numerical scheme. Finally, we present results for an aneurytic channel under both steady and pulsatile flow conditions. Comparisons are made with the results from an equivalent Newtonian fluid. Our choice of material parameters leads to only weakly elastic effects but noticeable differences are seen between the Newtonian and non-Newtonian flows, especially in the pulsating case.

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