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In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.

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A complementary experimental and numerical investigation was performed to study the three-dimensional flow structures and interactions of a finite-span synthetic jet in a crossflow at a chord-based Reynolds number of 100 000 and a 0 • angle of attack. Six blowing ratios in the range of 0.2-1.2 were considered. Experiments were conducted on a finite wing with a cross-sectional profile of NACA 4421, where particle-image velocimetry data were collected at the centre jet. To complement the experiments, three-dimensional numerical simulations were performed, where the numerical set-up matched not only the physical parameters (e.g. free stream) but also the physical dimensions (e.g. orientation and location of the jet. For the low blowing ratio cases, spatial non-uniformities developed, due to the finite span of the slit, which led to the formation of small and organized secondary structures or a streak-like pattern in the mean flow. On the other hand, for the high blowing ratio range, turbulent vortical structures were dominant, leading to larger spanwise structures, with a larger spanwise wavelength. Moreover, the phase-locked flow fields exhibited a train of counter-rotating coherent vortices that lifted off the surface as they advected downstream. In the mid-blowing ratio range, combined features of the low range (near the slit) and high range (in downstream locations) were found, where a pair of counter-rotating vortices issued in the same jet cycle collided with each other. In all cases, the spanwise extent of the secondary coherent structures reduced with downstream distance with a larger decrease at higher blowing ratios. Similar observations were made in earlier studies on finite-span synthetic jets in quiescent conditions.