AuthorOnkar Sahni
TitleAn Anisotropic Adaptive Procedure for Efficient Blood Flow Simulations
SchoolSchool of Engineering
InstitutionRensselaer Polytechnic Institute
AbstractDirectional features like boundary layers commonly arise in the solution of partial differential equations governing fluid flows. Such features can be resolved effciently by using anisotropic meshes. To automatically construct such a mesh requires an adaptive algorithm that provides information about the desired anisotropic mesh size field. In recent years, several researchers have considered and investigated procedures to construct anisotropic size field. To compute anisotropic element sizes over the domain we adopt the Hessian strategy. In this work, the Hessian strategy is based on the second derivatives of average flow field over a cardiac cycle due to the pulsatile nature of the flow in blood vessels.

This study presents an algorithm to perform anisotropic mesh adaptation in the simulation of blood flow in the cardiovascular system. The governing equations are the transient incompressible Navier-Stokes equations. We first apply the procedure to analytical cases and then to a real case of porcine aorta with a stenosis bypassed by a graft that involves real 3D curved geometry of blood vessels. We demonstrate that such a method results in an order of magnitude reduction in the computing time for a given level of accuracy making the method computationally efficient.

One of the quantities of physical interest in blood flow simulations is the wall shear stress (WSS). In this study we investigate the effect of the quality of meshes, obtained through anisotropic adaptive procedure, on WSS predictions. We demonstrate that controlling the mesh adaptation procedure in a way that maintains structured and graded elements near the wall leads to a more accurate WSS computation.

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