A discrete geometric approach for simulating the dynamics of thin viscous threads
A discrete geometric approach for simulating the dynamics of thin viscous threads
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DOI：
10.1016/j.jcp.2013.06.034
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发表时间：
2013-11-15
影响因子：
4.1
通讯作者：
Wardetzky, M.
中科院分区：
文献类型：
--
作者：
Audoly, B.;Clauvelin, N.;Wardetzky, M.
我们提出了一个数值模型的基础上离散的，拉格朗日制定的光滑方程的薄粘性线程的动态。该模型使用了一组压缩的坐标，称为中心线/旋转表示：将中心线的切线与材料框架的方向连接起来的运动学约束用于消除与旋转相关的三个自由度中的两个。基于离散微分几何和变分原理对扭转的描述，我们建立了一个完整的离散粘性螺纹模型，其中特别包括内部粘性应力的离散表示。一致性的离散模型与经典的，光滑的细线程方程正式成立。我们的数值方法进行了验证，对稳定卷取的参考解决方案。该方法使得能够以稳健和有效的方式模拟粘性细线的不稳定行为，包括惯性、拉伸、弯曲、扭转、大旋转和表面张力的组合效应。(C)2013 Elsevier Inc. All rights reserved.
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension. (C) 2013 Elsevier Inc. All rights reserved.