标题： 基于体积分数的高效二阶自适应方法将CAD几何插入六面体网格中 显示英文标题

标题： An Efficient Second-Order Adaptive Procedure for Inserting CAD Geometries into Hexahedral Meshes using Volume Fractions

摘要： 本文研究了将三维计算机辅助设计（CAD）几何体插入由六面体单元组成的网格中的问题，采用的是体积分数表示法。 提出了一种自适应的实现方法。 该方法分为两个步骤。 第一步使用k-d树执行空间加速。 第二步以类似于自适应网格细化（AMR）的方式对单个六面体进行细分，并在最细的细分级别上将CAD几何体线性（作为平面）逼近。 该方法只需要从CAD内核进行两次几何查询：确定所查询的空间坐标是否位于CAD几何体内或体外，以及确定给定空间坐标处CAD几何体表面上的最近点。 我们证明了对于足够光滑的几何体和足够细化的背景网格，该方法具有二阶精度。 通过几个验证测试展示了预期的精度，并通过几个典型的CAD几何体实例展示了该方法的有效性。 显示英文摘要

摘要： This paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The procedure consists of two steps. The first step performs spatial acceleration using a k-d tree. The second step involves subdividing individual hexahedra in an adaptive mesh refinement (AMR)-like fashion and approximating the CAD geometry linearly (as a plane) at the finest subdivision. The procedure requires only two geometric queries from a CAD kernel: determining whether or not a queried spatial coordinate is inside or outside the CAD geometry and determining the closest point on the CAD geometry's surface from a given spatial coordinate. We prove that the procedure is second-order accurate for sufficiently smooth geometries and sufficiently refined background meshes. We demonstrate the expected order of accuracy is achieved with several verification tests and illustrate the procedure's effectiveness for several exemplar CAD geometries.