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Mathematical Problems in Engineering
Volume 2015, Article ID 915973, 17 pages
Research Article

Numerical Simulation of the Generalized Newtonian Free Surface Flows by a Density Reinitialization SPH Method

1Department of Mathematics, School of Hydraulic, Energy and Power Engineering, Yangzhou University, Yangzhou 225002, China
2Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710129, China

Received 15 June 2014; Revised 22 October 2014; Accepted 23 October 2014

Academic Editor: Kim M. Liew

Copyright © 2015 Jinlian Ren et al. 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.


A periodic density reinitialization smoothed particle hydrodynamics (PDRI-SPH) method is proposed to treat the generalized Newtonian free surface flows, which is based on the concept of Taylor series expansion. Meanwhile, an artificial stress term is also presented and tested, for the purpose of eliminating the unphysical phenomenon of particle clustering in fluid stretching. The free surface phenomena of a Cross model droplet impacting and spreading on an inclined rigid plate at low impacting angles are investigated numerically using the proposed PDRI-SPH method. In particular, the effect of the surface inclination and the different regimes of droplet impact, spreading and depositing on an inclined surface, are illustrated; the influence of surface inclination on the tensile instability is also concerned. The numerical results show that the accuracy and the stability of the conventional SPH are all improved by the periodic density reinitialization scheme. All numerical results agree well with the available reference data.