Improved kernel gradient free-smoothed particle hydrodynamics and its applications to heat transfer problems

doi:10.1088/1674-1056/25/2/020202

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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