Metric field construction for anisotropic mesh adaptation with application to blood flow simulations

Abstract

The goal of this paper is to generate an anisotropic metric field suitable for cardiovascular geometries before a fluid simulation. Starting from a curvature map, an initial surface metric field is computed. This metric is used for anisotropic surface mesh adaptation and consecutively extended inside the volume in a frontal manner. The algorithm is based on the method proposed by Alauzet but replaces the metric intersection steps by an original metric 'blending'. This allows for a graded anisotropic volume mesh with a refinement layer close to the walls. The benefits of the resulting mesh are multiple: a reduced number of degrees of freedom, a priori refinement in areas with strong gradients of velocity and automatically increased resolution in regions with high surface curvature. The primal application of this method is in the domain of cardiovascular flows. Flow fields and derived quantities (wall shear stress) through a model bypass around a stenosed artery obtained on an adapted and standard isotropic mesh are compared. In addition, the mesh generation method is tested on a more complex patient-specific geometry. Values of computed wall shear stress are shown to be close to values obtained on anisotropic Hessian-adapted mesh, demonstrating the computational efficiency of the approach in comparison with adaptation based on error indicators derived from flow field.

Computing a high-dimensional euclidean embedding from an arbitrary smooth riemannian metric

“…Yamakawa and Shimada [YS00] proposed an ellipsoidal bubble packing method, but inserting or deleting particles / bubbles is necessary in the computation. In mechanical and biomedical engineering, anisotropic meshing is widely used in computational fluid dynamics (CFD) [FA05, AL16, LL16] and blood flow simulations [MGR13,SRM14]. However, their methods are numerical and error estimation-based approaches.…”

A Priori Anisotropic Mesh Adaptation on Implicitly Defined Surfaces

“…Mesh adaptation on surfaces is a topic of great interest in the scientific panorama due to its potential strong impact with a view to practical applications (see, e.g., [31,33] among the most recent papers) and, more generally, to the approximation of partial differential equations on manifolds. Despite the relevance of this research field, there are still few works dealing with a surface mesh adaptation driven by a rigorous error analysis, and they are essentially confined to an isotropic context [3,12,13,25,30].…”