Skeleton-based Block-structured Mesh Generation of Vascular Domains
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Patient-specific modeling has been growing in popularity in recent years, as a paradigm that offers a non-invasive manner of studying various health conditions, e.g., to perform analysis or support decision-making. A prominent example are simulations of aortic blood flow which are often based on the finite element method. As such, they require high-quality and surface-conforming meshes. This presents a difficult task, especially when considering aortas with pathologies, as they imply a plethora of topological and geometrical challenges. Examples include aneurysms, aortic dissections and coarctations. In this work, we consider a skeleton-based block-structured approach to generating hexahedral meshes of aortas. The input is a triangle surface mesh of the domain. Thereafter, a topological skeleton is generated to guide the generation of a block-structure, i.e., a coarse subdivision of the domain into blocks. Furthermore, an implicit surface description, in this case a signed distance function, provides a projection method to map points to the surface of the actual domain. Finally, transfinite maps combine the previously mentioned ingredients to generate a fully structured, possibly even higher-order, hexahedral mesh. The block-structure contains a small number of blocks, meaning local properties can be induced already at the coarse level, which is simpler and computationally more efficient than processing a large simulation-suitable mesh. An example is the consideration of boundary layers by inducing anisotropic mesh refinement, via mesh grading. Moreover, since our block-structured meshes can be generated with any resolution, they enable efficient use of the geometric multigrid methods, via a hierarchy of meshes. REFERENCES [1] Livesu, M., Muntoni, A., Puppo, E., Scateni, R., Skeleton-driven Adaptive Hexahedral Meshing of Tubular Shapes, Comput. Graph. Forum., Vol. 35. pp. 237-246, 2016. [2] Bosnjak, D., Pepe, A., Schussnig, R., Schmalstieg D., Fries T. P., Higher-order block-structured hex meshing of tubular structures. Eng. Comput., 2023. [3] Wesseling P., Oosterlee C.W., Geometric multigrid with applications to computational fluid dynamics, J. Comput. Appl. Math., Vol. 128 pp. 311-334, 2001.