AuthorO. Sahni, J. Mueller, K.E. Jansen, M.S. Shephard and C.A. Taylor
TitleEfficient Anisotropic Adaptive Discretization of the Cardiovascular System
AbstractWe present an anisotropic adaptive discretization method and demonstrate how computational efficiency can be increased when applying it to the simulation of cardiovascular flow. A SUPG stabilized FE-method is used to solve the incompressible Navier-Stokes equations using linear elements. The anisotropic size field is determined from the recovered Hessian of the solution field. To perform mesh adaptation, a single mesh metric field is constructed for the whole cardiac cycle. Two alternative approaches are applied, one in which a metric field is constructed based on the average flow whereas in the other approach the metric field is obtained by intersecting metric fields computed at a number of specified instants during the cycle. We further demonstrate that controlling the mesh adaptation procedure in a way that maintains structured and graded elements near the wall leads to a more accurate wall shear stress computation. We apply the method to the case of a 3D branching vessel model. The efficiency of our approach is measured by analyzing the wall shear stress, a challenging but important quantity in the understanding of cardiovascular disease. The anisotropic adaptivity based on metric intersection achieves an order of magnitude reduction in terms of degrees of freedom when compared to uniform refinement for a given level of accuracy.
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