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Chin. Phys. B, 2016, Vol. 25(2): 020202    DOI: 10.1088/1674-1056/25/2/020202
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Improved kernel gradient free-smoothed particle hydrodynamics and its applications to heat transfer problems

Juan-Mian Lei(雷娟棉) and Xue-Ying Peng(彭雪莹)
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
Abstract  Kernel gradient free-smoothed particle hydrodynamics (KGF-SPH) is a modified smoothed particle hydrodynamics (SPH) method which has higher precision than the conventional SPH. However, the Laplacian in KGF-SPH is approximated by the two-pass model which increases computational cost. A new kind of discretization scheme for the Laplacian is proposed in this paper, then a method with higher precision and better stability, called Improved KGF-SPH, is developed by modifying KGF-SPH with this new Laplacian model. One-dimensional (1D) and two-dimensional (2D) heat conduction problems are used to test the precision and stability of the Improved KGF-SPH. The numerical results demonstrate that the Improved KGF-SPH is more accurate than SPH, and stabler than KGF-SPH. Natural convections in a closed square cavity at different Rayleigh numbers are modeled by the Improved KGF-SPH with shifting particle positions, and the Improved KGF-SPH results are presented in comparison with those of SPH and finite volume method (FVM). The numerical results demonstrate that the Improved KGF-SPH is a more accurate method to study and model the heat transfer problems.
Keywords:  kernel gradient free-smoothed particle hydrodynamics      heat conduction      natural convection      accuracy and stability  
Received:  12 August 2015      Revised:  25 September 2015      Accepted manuscript online: 
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  44.10.+i (Heat conduction)  
  44.25.+f (Natural convection)  
Corresponding Authors:  Juan-Mian Lei     E-mail:  leijm@bit.edu.cn

Cite this article: 

Juan-Mian Lei(雷娟棉) and Xue-Ying Peng(彭雪莹) Improved kernel gradient free-smoothed particle hydrodynamics and its applications to heat transfer problems 2016 Chin. Phys. B 25 020202

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