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Particle mixing and reactive front motion in unsteady open shallow flow – Modelled using singular value decomposition

Lookup NU author(s): Professor Qiuhua Liang



Passive and active tracers are used to examine particle mixing and reactive front dynamics in an open shallow flow of water past a circular cylinder. A quadtree grid based Godunov-type shallow water equation solver predicts the unsteady flow hydrodynamics of the wake behind the cylinder. The resulting periodic flow field consisting of a von Kármán vortex street is decomposed and stored over one oscillatory period using Singular Value Decomposition (SVD). Particles are advected according to the reconstructed flow field from the SVD modes, with continuous spatial velocity information obtained via bilinear interpolation. Passive particle dynamics driven by different SVD flow modes is investigated, and it is found that the flow field recovered from the mean flow and the first pair of time varying modes is adequate to represent the complicated dynamical properties induced by the original flow field. Active autocatalytic reaction,A + B → 2B, is incorporated into the particle advection model, assuming surface reaction. Active particles are found to trace out an expanded version of the unstable manifold of the chaotic saddle in the wake, in qualitative agreement with published analytical results. The numerical model is applicable to mixing and transport processes in more complicated shallow environmental flows.

Publication metadata

Author(s): Liang Q, Taylor PH, Borthwick AGL

Publication type: Article

Publication status: Published

Journal: Computers & Fluids

Year: 2007

Volume: 36

Issue: 2

Pages: 248-258

ISSN (print): 0045-7930

ISSN (electronic): 1879-0747

Publisher: Pergamon


DOI: 10.1016/j.compfluid.2006.01.018


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