Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution

Ngo-Cong, D. and Mohammed, F. J. and Strunin, D. V. and Skvortsov, A. T. and Mai-Duy, N. and Tran-Cong, T. (2015) Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution. Journal of Hydrology, 525. pp. 87-101. ISSN 0022-1694

Abstract

The contaminant transport process governed by the advection–diffusion equation plays an important role in modelling industrial and environmental flows. In this article, our aim is to accurately reduce the 2-D advection–diffusion equation governing the dispersion of a contaminant in a turbulent open channel flow to its 1-D approximation. The 1-D model helps to quickly estimate the horizontal size of contaminant clouds based on the values of the model coefficients. We derive these coefficients analytically and investigate numerically the model convergence. The derivation is based on the centre manifold theory to
obtain successively more accurate approximations in a consistent manner. Two types of the average velocity profile are considered: the classical logarithmic profile and the power profile. We further develop the one-dimensional integrated radial basis function network method as a numerical approach to obtain the numerical solutions to both the original 2-D equation and the approximate 1-D equations. We compare the solutions of the original models with their centre-manifold approximations at very large
Reynolds numbers. The numerical results obtained from the approximate 1-D models are in good agreement with those of the original 2-D model for both the logarithmic and power velocity profiles


Statistics for USQ ePrint 28057
Statistics for this ePrint Item
Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to published version in accordance with the copyright policy of the publisher.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering
Date Deposited: 13 Nov 2015 05:44
Last Modified: 22 Feb 2017 00:47
Uncontrolled Keywords: contaminant transport; turbulent dispersion; open channel flow; centre manifolds; integrated radial basis functions; high-order approximation
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010399 Numerical and Computational Mathematics not elsewhere classified
Identification Number or DOI: 10.1016/j.jhydrol.2015.03.038
URI: http://eprints.usq.edu.au/id/eprint/28057

Actions (login required)

View Item Archive Repository Staff Only