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Hermite-DG methods for pdf equations modelling particle transport and deposition in turbulent boundary layers

Lookup NU author(s): Dr Peter van Dijk, Dr David Swailes


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A novel methodology is presented for the numerical treatment of multi-dimensional pdf (probability density function) models used to study particle transport in turbulent boundary layers. A system of coupled Fokker-Planck type equations is constructed to describe the transport of phase-space conditioned moments of particle and fluid velocities, both streamwise and wall-normal. This system, unlike conventional moment-based transport equations, allows for an exact treatment of particle deposition at the flow boundary and provides an efficient way to handle the 5-dimensional phase-space domain. Moreover, the equations in the system are linear and can be solved in a sequential fashion; there is no closure problem to address. A hybrid Hermite-Discontinuous Galerkin scheme is developed to treat the system. The choice of Hermite basis functions in combination with an iterative scaling approach permits the efficient computation of solutions to high accuracy. Results demonstrate the effectiveness of the methodology in resolving the extreme gradients characteristic of distributions near an absorbing boundary. (C) 2012 Elsevier Inc. All rights reserved.

Publication metadata

Author(s): van Dijk PJ, Swailes DC

Publication type: Article

Publication status: Published

Journal: Journal of Computational Physics

Year: 2012

Volume: 231

Issue: 14

Pages: 4904-4920

Print publication date: 17/04/2012

ISSN (print): 0021-9991

ISSN (electronic): 1090-2716

Publisher: Academic Press


DOI: 10.1016/


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Funder referenceFunder name
EP/D061601UK Engineering and Physical Sciences Research Council