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Pulsatile flow based on in vivo flow waveform

A computational fluid dynamics study was conducted by direct numerical simulation to elucidate three-dimensional complex flow structure with realistic pulsatile flow and geometry conditions based on animal study. The unsteady incompressible Navier-Stokes equations were solved using the spectral element method. The spectral element method is a high-order weighted residual technique and is ideally suited to flows at transitional Reynolds numbers as it results in minimal numerical dissipation and dispersion. Newtonian fluid behavior and rigid walls were assumed. Flow simulations were conducted on the NSF Pittsburgh Supercomputing Center TCS1 with 256 plus 1024 parallel processors (P). The simulations were initiated at Re << 1 and the Reynolds number was ramped up to the diastolic value by exponentially decreasing the viscosity. After initialization, the flow problem was simulated for six cardiac cycles with a polynomial degree of basis function N = 12. The volumetric flow rates measured in DVS and PVS during the animal study were phase-averaged for 12 heartbeat cycles. These flow waveforms were imposed as velocity boundary conditions with a Womersley solution which is an analytic solution of laminar fully developed pulsatile flow on both inlet boundaries. The minimum and maximum Reynolds numbers entering the graft, based on averaged velocities (over the cross-section) and graft diameter were 875 and 1235, respectively.