两类方程基本解的导出与验证(英文)

应用广义导数和Green公式,导出Laplace方程和热传导方程的基本解,并进行验证.最后举例说明了基本解的本质及应用.     

热传导界面问题的一种神经网络算法

本文讨论了一种单隐层神经网络算法在数值求解热传导界面问题中的应用。该算法设定含有神经网络函数的近似解满足初边值条件和Dirichlet 界面条件,通过求解由原方程导出的关于神经网络权重的离散优化问题来训练近似解中的神经网络,以使近似解逼近真解。文中也给出了一种基于随机梯度法思想的类随机梯度法来求解相应的离散优化问题。数值算例验证了算法的有效性。     

基于蒙特卡罗算法的高温作业防护服优化设计

高温作业防护服应具备较好的热防护性和使用性.在降低研发成本的条件下,对高温作业防护服的厚度值进行了优化求解.首先将三维的热传导过程简化为一维问题,立足于傅里叶热传导定律、稳态热传导方程、传热学原理等,建立了一维稳态热传导模型,得到了厚度、时间与温度差之间的关系.利用有限差分法求解出温度分布情况,误差分析结果验证了模型的可靠性.在满足约束条件的情况下,对防护服第2层与第4层厚度的最优设计采用蒙特卡罗算法,可避免陷入局部最优解,降低了研发成本,缩短了研发周期.同时,还可为相关高温作业防护服设计及其衍生产业发展提供参考.     

卷积型加权残值法求解梁的瞬态热传导问题

通过卷积将热传导方程构造成包含初始条件的新的具有完整初值问题特征的控制方程．对于新的控制方程以伽辽金加权残值法进行求解,经对梁的瞬态热传导问题的计算表明,该方法是一种精度好效率高的求解热传导同题的计算方法．     

线性热传导方程差分解的长时间行为

对带Dirichlet边值条件的线性热传导方程初边值问题采用两层差分离散格式生成的离散动力系统,证明了离散系统在L2(Ωh)和H10(Ωh)上吸引集的存在性,并得出离散系统解的长时间稳定性与收敛性.     

Effects of Carbon Content and Solidification Rate on the Thermal Conductivity of Grey Cast Iron

The thermal conductivity/diffusivity of pearlitic grey irons with various carbon contents was investigated by the laser flash method. The materials were cast in controlled thermal environments producing three dissimilar cooling rates. The cooling rates together with the carbon content largely influence the thermal conductivity of grey iron. Linear relationships exist between the thermal conductivity and the carbon content, the carbon equivalent, and the fraction of the former primary solidified austenite transformed into pearlite. The results show that the optimal thermal transport properties are obtained at medium cooling rates. Equations are given for the thermal conductivity of pearlite, solidified as pre-eutectic austenite, and the eutectic of grey iron. The thermal conductivity of pearlitic grey iron is modelled at both room temperature and elevated temperatures with good accuracy.     

求解热传导方程的四阶有限容积紧致格式

对非齐次热传导方程提出了一种数值求解的有限容积紧致格式,该格式具有空间上的四阶精度,且与有限差分紧致格式相比,更好地保持了问题的物理守恒性.数值算例表明,在相同的结点下,有限容积紧致格式比有限差分非紧致格式的精度更高.     

Molecular dynamics simulations of non-Fourier heat conduction

Unsteady heat conduction is known to deviate significantly from Fourier＇s law when the system time and length scales are within certain temporal and spatial windows of relaxation. Classical molecular dynamics simulations were used to investigate unsteady heat conduction in argon thin films with a sudden temperature increase or heat flux at one surface to study the non-Fourier heat conduction effects in argon thin films. The studies were conducted with both pure argon films and films with vacancy defects. The temperature profiles in the argon films showed the existence of mechanical waves when the thin film was suddenly heated and the wave nature of the heat propagation. The flux phase relaxation time, Zq, and the temperature phase relaxation time,τt, were calculated from the temporal variations of the energy flux and temperature distribution in the film. Comparisons of the MD temperature profiles with temperature profiles predicted by Fourier＇s law show that Fourier＇s law is not able to predict the temperature variations with time. Different film thicknesses were also studied to illustrate the variation of the time needed for the films to reach steady-state temperature profiles after a sudden temperature rise at one surface and to illustrate the finite speed of the energy waves.     

矩形网格抛物型问题的质量集中有限元方法

就一类典型的抛物型问题——热传导方程,研究矩形网格上质量集中有限元方法的有关性质.首先给出了矩形单元上双线性有限元基函数的积分公式,在此基础上讨论质量集中有限元方法的误差估计.研究表明,矩形网格上的质量集中有限元方法具有与普通的有限元方法同等的逼近精度,但却具有更少的计算量,并且在一定条件下可以保持极值性质.最后给出了在矩形网格上质量集中有限元方法保持极值性质的剖分条件.     

SPH原理、发展现状及热传导问题模型

对光滑粒子流体动力学方法（smoothed particle hydrodynamics,SPH）的基本技术原理及发展现状进行了综述,利用SPH方法对两个典型二维非线性动力学算例进行了数值模拟。同时,利用国外学者提出的方法初步探索了有关热传导问题的SPH模型。