Variational generation of prismatic boundary-layer meshes for biomedical computing

Boundary-layer meshes are important for numerical simulations in computational fluid dynamics, including computational biofluid dynamics of air flow in lungs and blood flow in hearts. Generating boundary-layer meshes is challenging for complex biological geometries. In this paper, we propose a novel technique for generating prismatic boundary-layer meshes for such complex geometries. Our method computes a feature size of the geometry, adapts the surface mesh based on the feature size, and then generates the prismatic layers by propagating the triangulated surface using the face-offsetting method. We derive a new variational method to optimize the prismatic layers to improve the triangle shapes and edge orthogonality of the prismatic elements and also introduce simple and effective measures to guarantee the validity of the mesh. Coupled with a high-quality tetrahedral mesh generator for the interior of the domain, our method generates high-quality hybrid meshes for accurate and efficient numerical simulations. We present comparative study to demonstrate the robustness and quality of our method for complex biomedical geometries.