Simulation of High Reynolds Number Vascular Flows

While much of the hemodynamics in a healthy human body has low Reynolds number, resulting in laminar flow, relatively high Reynolds number flow is observed at some specific locations, which can cause transition to turbulence. (The term “turbulence” refers to the motion of a fluid having local velocities and pressures that fluctuate randomly.) For example, the peak Reynolds number in the human aorta has been measured to be approximately 4000 [25]. Surgical constructions such as the arteriovenous (AV) graft, which consists of a prosthetic graft material surgically attached between an artery and a vein, also results in relatively high Reynolds number flow (1000–3000) [8,40]. Complex geometries such as a severe stenosis also can cause turbulent flow in the vasculature [22]. The simulation of turbulent vascular flows presents significant numerical challenges. Because such flows are only weakly turbulent, they lack an inertial subrange that is amenable to subgrid-scale modeling required for large-eddy or Reynolds-averaged NavierStokes simulations. The only reliable simulation approach at present is to directly resolve all scales of motion. While the Reynolds number is not high (Re=1000–2000, typ.), the physical dissipation is nonetheless small, and high-order methods are essential for efficiency. Moreover, turbulent blood flow exhibits a much broader range of scales than does its laminar (healthy) counterpart and thus requires an order of magnitude increase in spatial and temporal resolution. For example, recent work by Sherwin and Blackburn has shown that roughly one to two million gridpoints are required for spectral/spectralelement-based simulations of turbulence in an idealized stenosis [42].