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Article

Second-Order Symmetric Smoothed Particle Hydrodynamics Method for Transient Heat Conduction Problems with Initial Discontinuity

1
School of Mathematics, Tianjin University, Tianjin 300350, China
2
School of Civil Engineering, Tianjin University, Tianjin 300350, China
3
College of Intelligence and Computing, Tianjin University, Tianjin 300350, China
*
Author to whom correspondence should be addressed.
Processes 2018, 6(11), 215; https://doi.org/10.3390/pr6110215
Received: 21 September 2018 / Revised: 19 October 2018 / Accepted: 23 October 2018 / Published: 2 November 2018
(This article belongs to the Section Process Control and Supervision)
To eliminate the numerical oscillations appearing in the first-order symmetric smoothed particle hydrodynamics (FO-SSPH) method for simulating transient heat conduction problems with discontinuous initial distribution, this paper presents a second-order symmetric smoothed particle hydrodynamics (SO-SSPH) method. Numerical properties of both SO-SSPH and FO-SSPH are analyzed, including truncation error, numerical accuracy, convergence rate, and stability. Experimental results show that for transient heat conduction with initial smooth distribution, both FO-SSPH and SO-SSPH can achieve second-order convergence, which is consistent with the theoretical analysis. However, for one- and two-dimensional conduction with initial discontinuity, the FO-SSPH method suffers from serious unphysical oscillations, which do not disappear over time, and hence it only achieves first-order convergence; while the present SO-SSPH method can avoid unphysical oscillations and has second-order convergence rate. Therefore, the SO-SSPH method is a feasible tool for solving transient heat conduction problems with both smooth and discontinuous distributions, and it is easy to be extended to high dimensional cases. View Full-Text
Keywords: transient heat conduction; discontinuous distribution; smoothed particle hydrodynamics; convergence rate transient heat conduction; discontinuous distribution; smoothed particle hydrodynamics; convergence rate
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MDPI and ACS Style

Song, Z.; Xing, Y.; Hou, Q.; Lu, W. Second-Order Symmetric Smoothed Particle Hydrodynamics Method for Transient Heat Conduction Problems with Initial Discontinuity. Processes 2018, 6, 215. https://doi.org/10.3390/pr6110215

AMA Style

Song Z, Xing Y, Hou Q, Lu W. Second-Order Symmetric Smoothed Particle Hydrodynamics Method for Transient Heat Conduction Problems with Initial Discontinuity. Processes. 2018; 6(11):215. https://doi.org/10.3390/pr6110215

Chicago/Turabian Style

Song, Zhanjie, Yaxuan Xing, Qingzhi Hou, and Wenhuan Lu. 2018. "Second-Order Symmetric Smoothed Particle Hydrodynamics Method for Transient Heat Conduction Problems with Initial Discontinuity" Processes 6, no. 11: 215. https://doi.org/10.3390/pr6110215

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