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Water 2017, 9(2), 132; doi:10.3390/w9020132

SPH Simulations of Solute Transport in Flows with Steep Velocity and Concentration Gradients

1
Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei City 106, Taiwan
2
Hydrotech Research Institute, National Taiwan University, Taipei City 106, Taiwan
*
Author to whom correspondence should be addressed.
Academic Editors: Gordon Huang and Yurui Fan
Received: 7 December 2016 / Revised: 6 February 2017 / Accepted: 14 February 2017 / Published: 17 February 2017
(This article belongs to the Special Issue Modeling of Water Systems)
View Full-Text   |   Download PDF [5098 KB, uploaded 17 February 2017]   |  

Abstract

In this study, a meshless particle method, smoothed particle hydrodynamics (SPH), is adopted to solve the shallow water equations (SWEs) and the advection diffusion equations (ADEs) for simulating solute transport processes under 1D/2D conditions with steep gradients. A new SPH-SWEs-ADEs model is herein developed to focus on the numerical performance of solute transport in flows with steep velocity and concentration gradients, since the traditional mesh-based methods have numerical difficulties on solving such steep velocity/concentration gradient flows. The present model is validated by six benchmark study cases, including three steep concentration gradient cases and three coupled steep concentration/velocity gradient cases. The comparison between the simulated results and the exact solutions for the former three cases shows that complete mass concentration conservation in pure advection-dominated flows is preserved. The numerical oscillation in concentration and the negative concentration resulted from the discretization of the advection term of ADEs can be totally avoided. The other three cases confirm that this model can also well capture coupled steep gradients of velocities and concentrations. It is demonstrated that the presented solver is an effective and reliable tool to investigate solute transports in complex flows incorporating steep velocity gradients. View Full-Text
Keywords: smoothed particle hydrodynamics; shallow water equations; advection diffusion equations; steep concentration gradient; steep velocity gradient smoothed particle hydrodynamics; shallow water equations; advection diffusion equations; steep concentration gradient; steep velocity gradient
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Chang, Y.-S.; Chang, T.-J. SPH Simulations of Solute Transport in Flows with Steep Velocity and Concentration Gradients. Water 2017, 9, 132.

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