Numerical simulation of fluid mechanical phenomena in idealised physiological geometries : stenosis and double bend

Abstract

The spectral/hp element numerical technique is applied to the direct numerical simulation (DNS) and linearised stability analysis of fluid flow in two geometries of fundamental fluid mechanical interest, each with relevance to biomechanical flow. The fluid model is that of incompressible. Newtonian, viscous flow in rigid geometries. The first model, that of a three dimensional tube with a reflex double 45° bend is subject to a fully three-dimensional DNS analysis. This model serves as an idealised artery model, relevant to curved arteries and as an extremely simplified peripheral artery graft model. The persistence of the first Dean vortex pair at higher Reynolds number, as observed by Hoogstraten et al., is again observed, and qualitative explanation is offered by examination of the generation and annihilation of axial vorticity. In addition, results are presented of an unsteady analysis subject to Womersley inflow. Higher frequency results display the shedding of new horseshoe vortical structures. The second model is that of a two dimensional simplified constricted artery model, subjected to a BiGlobal linearised stability analysis. Two new three-dimensional saturated steady states are located for steady flows in a symmetric geometry, and one for an asymmetric geometry. In addition, the Floquet analysis of pulsatile flow is performed upon both symmetric and asymmetric geometries, with primary instabilities located, neutral stability curves presented and Floquet modes and saturated three-dimensional flow cycles obtained.