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Efficient anisotropic adaptive discretization of the cardiovascular system. (English) Zbl 1125.76046

Summary: We present an anisotropic adaptive discretization method and demonstrate how computational efficiency can be increased when applying it to the simulation of cardiovascular flow. We further propose a new adaptive approach which controls the mesh adaptation procedure to maintain structured and graded elements near the wall resulting in a more accurate wall shear stress computation. To perform mesh adaptation for hemodynamic flows, 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 specified instants in the cycle. 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 general anisotropic adaptivity based on metric intersection achieves over an order of magnitude reduction in terms of degrees of freedom when compared to uniform refinement for a given level of accuracy.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76Z05 Physiological flows
92C35 Physiological flow
92-08 Computational methods for problems pertaining to biology
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