Numerical Considerations for Lagrangian Stochastic Dispersion Models: Eliminating Rogue Trajectories, and the Importance of Numerical Accuracy

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• 作者：Brian N. Bailey
• 关键词：Lagrangian stochastic dispersion models ; Large ; eddy simulation ; Rogue trajectories ; Turbulent dispersion
• 刊名：Boundary-Layer Meteorology
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：162
• 期：1
• 页码：43-70
• 全文大小：
• 刊物类别：Earth and Environmental Science
• 刊物主题：Atmospheric Sciences; Meteorology; Atmospheric Protection/Air Quality Control/Air Pollution;
• 出版者：Springer Netherlands
• ISSN：1573-1472
• 卷排序：162

文摘

When Lagrangian stochastic models for turbulent dispersion are applied to complex atmospheric flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behaviour in the numerical solution. Here we discuss numerical strategies for solving the non-linear Langevin-based particle velocity evolution equation that eliminate such unphysical behaviour in both Reynolds-averaged and large-eddy simulation applications. Extremely large or ‘rogue’ particle velocities are caused when the numerical integration scheme becomes unstable. Such instabilities can be eliminated by using a sufficiently small integration timestep, or in cases where the required timestep is unrealistically small, an unconditionally stable implicit integration scheme can be used. When the generalized anisotropic turbulence model is used, it is critical that the input velocity covariance tensor be realizable, otherwise unphysical behaviour can become problematic regardless of the integration scheme or size of the timestep. A method is presented to ensure realizability, and thus eliminate such behaviour. It was also found that the numerical accuracy of the integration scheme determined the degree to which the second law of thermodynamics or ‘well-mixed condition’ was satisfied. Perhaps more importantly, it also determined the degree to which modelled Eulerian particle velocity statistics matched the specified Eulerian distributions (which is the ultimate goal of the numerical solution). It is recommended that future models be verified by not only checking the well-mixed condition, but perhaps more importantly by checking that computed Eulerian statistics match the Eulerian statistics specified as inputs.