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为了解决传统光滑粒子动力学（SPH）方法求解三维变系数瞬态热传导方程时出现的精度低、稳定性差和计算效率低的问题，本文首先基于Taylor展开思想拓展一阶对称SPH方法到三维热传导问题的模拟，其次引入稳定化处理的迎风思想，最后基于相邻粒子标记和MPI并行技术，结合边界处理方法得到一种能够准确、高效地求解三维变系数瞬态热传导问题的修正并行SPH方法.通过对带有Direclet和Newmann边界条件的常/变系数三维热传导方程进行模拟，并与解析解进行对比，对提出的方法的精度、收敛性及计算效率进行了分析；随后，运用提出的修正并行SPH方法对三维功能梯度材料中温度变化进行了模拟预测，并与其他数值结果做对比，准确地展现了功能梯度材料中温度变化过程.
[1] Zhang Z, Wang J F, Cheng Y M, Liew K M 2013 Sci. China 56 1568
[2] Sutradhar A, Paulino G H, Gray J J 2002 Engin. Anal. Bound. Elements 26 119
[3] Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[4] Zhang J Q, Niea L, Zhang X Y, Chen R Y 2014 Eur. Phys. J. B 87 285
[5] Nie L R, Yu L L, Zheng Z G, Shu C Z 2013 Phys. Rev. E 87 062142
[6] Lewis R W, Nithiarasu P, Seetharamu K N 2004 Fundamentals of the Finite Element Method for Heat and Fluid Flow (Chichester:John Wiley)
[7] Akil J H 2008 J. Computat. Appl. Math. 220 335
[8] Zhong C W, Xie J F, Zhuo C S, Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[9] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[10] Liu M B, Liu G R 2010 Arch. Computat. Methods Engin. 17 25
[11] Jeong J H, Jhon M S, Halow J S, Osdol J V 2003 Comput. Phys. Commun. 153 71
[12] Chen J K, Beraun J E, Carney T C 1999 Int. J. Num. Meth. Eng. 46 231
[13] Zhang G M, Batra R C 2004 Comp. Mech. 34 137
[14] Bonet J, Lok T S L 1999 Comput. Meth. Appl. Mech. Eng. 180 97
[15] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese)[刘谋斌, 常建忠 2010 物理学报 59 3654]
[16] Liu M B, Liu G R 2006 Appl. Num. Math. 56 19
[17] Jiang T, Ouyang J, Li X J, Zhang L, Ren J L 2011 Acta Phys. Sin. 60 090206 (in Chinese)[蒋涛, 欧阳洁, 栗雪娟, 张林, 任金莲 2011 物理学报 60 090206]
[18] Holman J P 2002 Heat Transfer (9th Ed.) (Singapore:McGraw-Hill)
[19] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics:A Mesh-free Particle Method (Singapore:World Scientific)
[20] Young D L, Tsai C C, Murugesan K, Fan C M, Chen C 2004 Engin. Anal. Bound. Elements 28 1463
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[1] Zhang Z, Wang J F, Cheng Y M, Liew K M 2013 Sci. China 56 1568
[2] Sutradhar A, Paulino G H, Gray J J 2002 Engin. Anal. Bound. Elements 26 119
[3] Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[4] Zhang J Q, Niea L, Zhang X Y, Chen R Y 2014 Eur. Phys. J. B 87 285
[5] Nie L R, Yu L L, Zheng Z G, Shu C Z 2013 Phys. Rev. E 87 062142
[6] Lewis R W, Nithiarasu P, Seetharamu K N 2004 Fundamentals of the Finite Element Method for Heat and Fluid Flow (Chichester:John Wiley)
[7] Akil J H 2008 J. Computat. Appl. Math. 220 335
[8] Zhong C W, Xie J F, Zhuo C S, Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[9] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[10] Liu M B, Liu G R 2010 Arch. Computat. Methods Engin. 17 25
[11] Jeong J H, Jhon M S, Halow J S, Osdol J V 2003 Comput. Phys. Commun. 153 71
[12] Chen J K, Beraun J E, Carney T C 1999 Int. J. Num. Meth. Eng. 46 231
[13] Zhang G M, Batra R C 2004 Comp. Mech. 34 137
[14] Bonet J, Lok T S L 1999 Comput. Meth. Appl. Mech. Eng. 180 97
[15] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese)[刘谋斌, 常建忠 2010 物理学报 59 3654]
[16] Liu M B, Liu G R 2006 Appl. Num. Math. 56 19
[17] Jiang T, Ouyang J, Li X J, Zhang L, Ren J L 2011 Acta Phys. Sin. 60 090206 (in Chinese)[蒋涛, 欧阳洁, 栗雪娟, 张林, 任金莲 2011 物理学报 60 090206]
[18] Holman J P 2002 Heat Transfer (9th Ed.) (Singapore:McGraw-Hill)
[19] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics:A Mesh-free Particle Method (Singapore:World Scientific)
[20] Young D L, Tsai C C, Murugesan K, Fan C M, Chen C 2004 Engin. Anal. Bound. Elements 28 1463
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