arXiv 2406.182432024-06physics.flu-dynphysics.ao-ph

使用指数滤波器的高效拉格朗日平均

Efficient Lagrangian averaging with exponential filters

Abhijeet Minz, Lois E. Baker, Hossein A. Kafiabad, Jacques Vanneste

AI总结：

针对流体动力学中拉格朗日平均数值计算成本高的问题，提出一种基于演化PDE单次求解的方法，利用指数和滤波器实现即时计算，有效滤除大振幅Poincaré波并保留湍流特征。

摘要：

拉格朗日平均是分析和建模流体动力学中多尺度过程的重要工具。然而，从模拟数据中数值计算拉格朗日（时间）平均具有挑战性。它可以通过追踪大量粒子来实现，或者按照近期的一种方法，通过求解一组专门的偏微分方程（PDEs）来实现。这两种方法计算量都很大，因为对于需要拉格朗日平均场的每一个时间点，它们都需要进行一次全新的计算。我们通过开发一种基于PDE的方法克服了这一缺点，该方法通过演化PDE的一次求解即可提供所有时间的拉格朗日平均场。这使得即时实现成为可能，即拉格朗日平均与动力学变量一同计算。这得益于使用一类特殊的时间滤波器，其核是指数函数之和。我们关注涉及一个和两个指数函数的两个特定核。我们在旋转浅水模型中实现了这些核，并证明了它们在滤除大振幅Poincaré波的同时保留底层缓慢演化湍流显著特征的有效性。

英文摘要：

Lagrangian averaging is a valuable tool for the analysis and modelling of multiscale processes in fluid dynamics. The numerical computation of Lagrangian (time) averages from simulation data is challenging, however. It can be carried out by tracking a large number of particles or, following a recent approach, by solving a dedicated set of partial differential equations (PDEs). Both approaches are computationally demanding because they require an entirely new computation for each time at which the Lagrangian mean fields are desired. We overcome this drawback by developing a PDE-based method that delivers Lagrangian mean fields for all times through the single solution of evolutionary PDEs. This allows for an on-the-fly implementation, in which Lagrangian averages are computed along with the dynamical variables. This is made possible by the use of a special class of temporal filters whose kernels are sums of exponential functions. We focus on two specific kernels involving one and two exponential functions. We implement these in the rotating shallow-water model and demonstrate their effectiveness at filtering out large-amplitude Poincaré waves while retaining the salient features of an underlying slowly evolving turbulent flow.

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