中文摘要：

为提高传统光滑粒子动力学（smoothed particle hydrodynamics,SPH）方法模拟瞬态热传导问题的精度和稳定性,本文提出了一种一阶对称光滑粒子动力学（first order symmetric SPH,FO-SSPH）方法.该方法将具有二阶热传导方程分解成两个一阶偏微分方程,然后基于梯度离散和Taylor级数展开思想,对一阶核梯度形式进行修正,并将得到的局部矩阵对称化.数值结果表明：与传统SPH方法相比,FO-SSPH方法精度高、数值稳定性好;该方法能较准确地直接施加混合边值条件,且求解多边值抛物型偏微分问题可靠、灵活.文中最后运用FO-SSPH方法研究了一维非线性热传导问题趋近稳态时温度分布出现的＂凹＂、＂凸＂奇异现象,并讨论了热流系数对＂凹＂、＂凸＂现象的影响.

英文摘要：

In order to improve the accuracy and the stability of the conventional smoothed particle hydrodynamics （SPH） method for simulating the transient heat conduction problems, a first order symmetric smoothed particle hydrodynamics （FO-SPH） method is proposed.In order to solve the heat conduction problem with second derivative, the proposed FO-SSPH method is first to decompose the problem into two first order partial differential equations （PDEs）, and then the first order kernel gradient is corrected based on the discretization of gradient and the concept of Taylor series. Finally, the obtained local matrix is locally symmetrized. All the numerical results demonstrate that the FO-SSPH possesses a higher accuracy and better stability than the SPH method, that the mixed boundary conditions can be well imposed using FO-SSPH method, and that the reliability and the flexibility of the FO-SSPH method can also be observed for PDEs with multi-boundary conditions. Finally, the one-dimensional nonlinear heat conduction problem is investigated by the FO-SSPH method, and the phenomena of concave and bulge are observed when the temperature achieves the stable state, in which the influence of the coefficients for heat flux is discussed.