Hidden Degrees of Freedom in Implicit Vortex Filaments
Hidden Degrees of Freedom in Implicit Vortex Filaments
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DOI：
10.1145/3550454.3555459
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Sadashige Ishida;C. Wojtan;Albert Chern
中科院分区：
文献类型：
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作者：
Sadashige Ishida;C. Wojtan;Albert Chern
本文提出了一种新的曲线动力学表示方法，并将其应用于流体动力学中的涡丝。代替用显式曲线几何和拉格朗日运动方程来表示这些细丝，我们用一种新的协维2水平集描述隐式地表示曲线。我们的隐式表示在曲线的结构和动力学方面都允许几个冗余的数学自由度，可以专门定制以提高数值鲁棒性，与遭受压倒性数值稳定性问题的隐式曲线动力学的朴素方法相反。此外，我们注意到这些隐藏的自由度如何完美地映射到流体动力学中的克莱施表示。在这些观察结果的激励下，我们引入了非扭曲水平集函数和非旋转动力学，它们成功地正则化了数值不稳定性的来源，特别是在曲线细丝周围的扭曲模式中。其结果是一种新的模拟方法，可以为大量相互作用的涡丝产生稳定的动力学，并且可以毫不费力地处理拓扑变化和重新连接事件。
This paper presents a new representation of curve dynamics, with applications to vortex filaments in fluid dynamics. Instead of representing these filaments with explicit curve geometry and Lagrangian equations of motion, we represent curves implicitly with a new co-dimensional 2 level set description. Our implicit representation admits several redundant mathematical degrees of freedom in both the configuration and the dynamics of the curves, which can be tailored specifically to improve numerical robustness, in contrast to naive approaches for implicit curve dynamics that suffer from overwhelming numerical stability problems. Furthermore, we note how these hidden degrees of freedom perfectly map to a Clebsch representation in fluid dynamics. Motivated by these observations, we introduce untwisted level set functions and non-swirling dynamics which successfully regularize sources of numerical instability, particularly in the twisting modes around curve filaments. A consequence is a novel simulation method which produces stable dynamics for large numbers of interacting vortex filaments and effortlessly handles topological changes and re-connection events.