A Modified Double Gyre with Ground Truth Hyperbolic Trajectories for Flow Visualization,Computer Graphics Forum

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A Modified Double Gyre with Ground Truth Hyperbolic Trajectories for Flow Visualization
Computer Graphics Forum ( IF 2.7 ) Pub Date : 2020-12-22 , DOI: 10.1111/cgf.14183
S. Wolligandt ₁ , T. Wilde ₁ , C. Rössl ₁ , H. Theisel ₁

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The model of a Double Gyre flow by Shadden et al. is a standard benchmark data set for the computation of hyperbolic Lagrangian Coherent Structures (LCS) in flow data. While structurally extremely simple, it generates hyperbolic LCS of arbitrary complexity. Unfortunately, the Double Gyre does not come with a well‐defined ground truth: the location of hyperbolic LCS boundaries can only be approximated by numerical methods that usually involve the gradient of the flow map. We present a new benchmark data set that is a small but carefully designed modification of the Double Gyre, which comes with ground truth closed‐form hyperbolic trajectories. This allows for computing hyperbolic LCS boundaries by a simple particle integration without the consideration of the flow map gradient. We use these hyperbolic LCS as a ground truth solution for testing an existing numerical approach for extracting hyperbolic trajectories. In addition, we are able to construct hyperbolic LCS curves that are significantly longer than in existing numerical methods.

中文翻译：

具有地面真相双曲轨迹的改进双回转流可视化

Shadden等人的双回转流模型。是用于计算流量数据中双曲型拉格朗日相干结构（LCS）的标准基准数据集。尽管在结构上极其简单，但它会生成任意复杂度的双曲LCS。不幸的是，Double Gyre并没有一个明确的基本事实：双曲线LCS边界的位置只能通过通常涉及流图梯度的数值方法来近似。我们提供了一个新的基准数据集，该数据集是Double Gyre的一个很小但经过精心设计的修改，它带有地面实数闭合形式的双曲线轨迹。这允许通过简单的粒子积分来计算双曲LCS边界，而无需考虑流图梯度。我们将这些双曲线LCS用作地面真值解决方案，以测试提取双曲线轨迹的现有数值方法。此外，我们能够构造比现有数值方法更长的双曲线LCS曲线。

更新日期：2021-02-24

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