Variational construction of tubular and toroidal streamsurfaces for flow visualization

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-03-13 DOI:10.1098/rspa.2023.0951
Mingwu Li, Bálint Kaszás, George Haller
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Abstract

Approximate streamsurfaces of a three-dimensional velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces enable effective and efficient visualization of vortical regions in three-dimensional flows. Here we propose a variational construction of these approximate streamsurfaces to remove the limitation of Fourier series representation of the first integral in earlier work. Specifically, we use finite-element methods to solve a partial differential equation that describes the best approximate first integral for a given velocity field. We use several examples to demonstrate the power of our approach for three-dimensional flows in domains with arbitrary geometries and boundary conditions. These include generalized axisymmetric flows in the domains of a sphere (spherical vortex), a cylinder (cylindrical vortex) and a hollow cylinder (Taylor–Couette flow) as benchmark studies for various computational domains, non-integrable periodic flows (ABC and Euler flows) and Rayleigh–Bénard convection flows. We also illustrate the use of the variational construction in extracting momentum barriers in Rayleigh–Bénard convection.

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用于流动可视化的管状和环状流面的变量构造
三维速度场的近似流面最近被构建为速度场最接近的第一积分等值面。这种近似流场曲面可以有效、高效地显示三维流动中的涡流区域。在这里,我们提出了这些近似流曲面的变分构造,以消除早期工作中傅里叶级数表示第一积分的限制。具体来说,我们使用有限元方法求解一个偏微分方程,该方程描述了给定速度场的最佳近似第一积分。我们用几个例子来展示我们的方法在具有任意几何形状和边界条件的域中进行三维流动时的威力。这些例子包括球体(球形漩涡)、圆柱体(圆柱形漩涡)和空心圆柱体(泰勒-库埃特流)域中的广义轴对称流动(作为各种计算域的基准研究)、不可积分周期流(ABC 和欧拉流)以及瑞利-贝纳德对流。我们还说明了在提取瑞利-贝纳德对流中的动量势垒时如何使用变分结构。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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