论文标题
隐性涡旋细丝中隐藏的自由度
Hidden Degrees of Freedom in Implicit Vortex Filaments
论文作者
论文摘要
本文介绍了曲线动力学的新表示，并在流体动力学中应用于涡旋细丝。我们没有用明确的曲线几何形状和拉格朗日运动方程表示这些细丝，而是用新的Co new conimenitional 2级集合描述暗示曲线。我们的隐式表示在曲线的配置和动力学中都承认了几种冗余的数学自由度，可以专门量身定制以提高数值鲁棒性，而天真的方法对于隐式曲线动力学而言，这些动力学因倒入数值稳定性问题而遭受的隐式曲线动力学。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Clebsch表示。在这些观察结果的激励下，我们引入了不扭曲的级别集合功能和非旋转动力学，这些函数成功地使数值不稳定性的来源正规化了，尤其是在曲线丝的扭曲模式下。结果是一种新型的模拟方法，该方法可为大量相互作用的涡流丝产生稳定的动力学，并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.
