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首页> 外文期刊>Journal of Computational Physics >A front-tracking method with Catmull-Clark subdivision surfaces for studying liquid capsules enclosed by thin shells in shear flow
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A front-tracking method with Catmull-Clark subdivision surfaces for studying liquid capsules enclosed by thin shells in shear flow

机译：Catmull-Clark细分曲面的前向跟踪方法，用于研究剪切流中被薄壳包裹的液体胶囊

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摘要

This paper presents a front-tracking method for studying the large deformation of a liquid capsule enclosed by a thin shell in a shear flow. The interaction between the fluid and the shell body is accomplished through an implicit immersed boundary method. An improved thin-shell model for computing the forces acting on the shell middle surface during the deformation is described in surface curvilinear coordinates and within the framework of the principle of virtual displacements. This thin-shell model takes full account of in-plane tensions and bending moments developing due to the shell thickness and a preferred three-dimensional membrane structure. The approximation of the shell middle surface is performed through the use of the Catmull-Clark subdivision surfaces. The resulting limit surface is C~2-continuous everywhere except at a small number of extraordinary nodes where it retains C~1 continuity. The smoothness of the limit surface significantly improves the ability of our method in simulating capsules enclosed by hyperelastic thin shells with different shapes and physical properties. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical, ellipsoidal and biconcave capsules in the shear flow. In addition, different types of motion such as tank-treading, swinging, tumbling and transition from tumbling to swinging have been studied over a range of shear rates, viscosity ratios and bending modulus.
机译：本文提出了一种前向跟踪方法，用于研究剪切流中被薄壳包裹的液体囊的大变形。流体与壳主体之间的相互作用是通过隐式浸入边界方法实现的。在曲面曲线坐标中并在虚拟位移原理的框架内，描述了一种改进的薄壳模型，用于计算变形过程中作用在壳中间表面上的力。这种薄壳模型充分考虑了由于壳厚度和优选的三维膜结构而产生的平面内张力和弯矩。通过使用Catmull-Clark细分曲面可以对壳体中间表面进行逼近。最终的极限曲面在所有地方都是C〜2连续的，除了少数保留C〜1连续性的非寻常节点。极限表面的光滑度显着提高了我们的方法对具有不同形状和物理特性的超弹性薄壳所包围的胶囊进行模拟的能力。本数值技术已通过几个实例得到验证，包括球形壳的膨胀以及剪切流中球形，椭圆形和双凹面胶囊的变形。另外，已经在剪切速率，粘度比和弯曲模量的范围内研究了不同类型的运动，例如踩踏，摆动，翻滚以及从翻滚到摆动的过渡。

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