Instability in Lagrangian Stochastic Trajectory Models, and a Method for its Cure


  1. Yee, E.
  2. Wilson, J.D.
Corporate Authors
Defence R&D Canada - Suffield, Ralston ALTA (CAN)
A number of authors have reported the problem of unrealistic velocities ("rogue trajectories") when computing the paths of particles in a turbulent flow using modern Lagrangian stochastic (LS) models, and have resorted to ad hoc interventions. We suggest that this problem stems from two causes: (1) unstable modes that are intrinsic to the dynamical system constituted by the generalized Langevin equations, and whose actual triggering (expression) is conditional on the fields of the mean velocity and Reynolds stress tensor and is liable to occur in complex, disturbed flows (which, if computational, will also be imperfect and discontinuous); and, (2) the "stiffness" of the generalized Langevin equations, which implies that the simple stochastic generalization of the Euler scheme usually used to integrate these equations is not sufficient to keep round-off errors under control. These two causes are connected, with the first cause (dynamical instability) exacerbating the second (numerical instability); removing the first cause does not necessarily correct the second, and vice versa. To overcome this problem, we introduce a fractional-step integration scheme that splits the velocity increment into contributions that are linear (Ui) and nonlinear (UiUj) in the Lagrangian velocity fluctuation vector U, the nonlinear contribution being further split into its diagonal and off-diagonal parts. The linear contribution and the diagonal part of the nonlinear
Lagrangian stochastic models;Markov chain Monte Carlo;Source reconstruction
Report Number
DRDC-SUFFIELD-SL-2006-133 — Scientific Literature
Date of publication
21 Oct 2006
Number of Pages
Reprinted from
Springer Science+Business Media,Boundary-Layer Meteorol, Vol 122, 2007, p243-261
Hardcopy;Document Image stored on Optical Disk

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