Abstract In this paper, we develop a scalable, adaptively refined, octree-based finite element approach with immersogeometric analysis to track inertial migration of particles in microchannels. Fluid physics is modeled using a residual-based variational multiscale method, and the particle movement is modeled as rigid body motion. A parallel, hierarchically refined octree mesh is employed as the background mesh, on which a variationally consistent immersogeometric formulation is adopted for tracking the particle motion in the fluid. Adaptations of immersogeometric analysis on an octree background mesh are developed to enable efficient searching of background element for a given surface quadrature point, as well as a distribution of surface quadrature points over processors to reduce memory overhead and better parallelize the surface assembly. An octree-based adaptive mesh refinement algorithm adapted to in-out test in the immersogeometric approach is also developed. The validation of our octree-based immersogeometric approach is carried out using a benchmark case of a sphere settling in quiescent fluid, with good agreement presented. In addition, good strong (and weak) scalability on supercomputing resources for this benchmark case up to 16,384 processes is demonstrated. The proposed method is further deployed for exploring particle migration in straight and converging-diverging channels. This example illustrates the potential of the octree-based immersogeometric approach for efficiently tracking particle motion in complex channel flows – a problem with a diverse array of applications.

中文翻译：

---

一种基于八叉树的浸入几何方法，用于模拟通道中粒子的惯性迁移

摘要在本文中，我们开发了一种可扩展的、自适应改进的、基于八叉树的有限元方法，采用浸入式几何分析来跟踪微通道中粒子的惯性迁移。流体物理使用基于残差的变分多尺度方法建模，粒子运动建模为刚体运动。采用平行的、分层细化的八叉树网格作为背景网格，在其上采用变分一致的浸没几何公式来跟踪流体中的粒子运动。开发了对八叉树背景网格的浸入几何分析的适应性，以实现对给定表面正交点的背景元素的有效搜索，以及表面正交点在处理器上的分布，以减少内存开销并更好地并行化表面组件。还开发了一种基于八叉树的自适应网格细化算法，适用于浸入式几何方法中的输入输出测试。我们的基于八叉树的浸没几何方法的验证是使用球体在静止流体中沉降的基准案例进行的，并且呈现出良好的一致性。此外，该基准案例的超级计算资源具有良好的强（和弱）可扩展性，最多 16,384 个进程。所提出的方法进一步用于探索直通道和会聚-发散通道中的粒子迁移。这个例子说明了基于八叉树的浸入几何方法在复杂通道流中有效跟踪粒子运动的潜力——这是一个广泛应用的问题。