摘要
光滑粒子法是近些年来发展起来的一种新的数值计算方法,已经成功应用到多种工程和物理问题的求解中.为修正光滑粒子法计算域边界附近粒子近似缺陷及弥补边界条件处理方法的不足,将有限差分法耦合到光滑粒子法中,使所求解问题在整个计算域上的函数近似精度达到二阶,从而提高计算的求解精度;然后基于有限差分算法处理边界条件的思想来处理定解问题中的第二、第三类边界条件,使复杂边值问题的计算可以归于第一类边值问题的框架下求解.采用光滑粒子-有限差分耦合算法计算了各类不同边界条件下的导热问题,通过和解析解的对比表明,相比传统光滑粒子法,耦合算法能够直接施加各类边界条件,计算结果精度高,求解过程可靠有效.最后模拟了非饱和岩土介质内的热能传输问题,得到了岩土介质中随时间变化的温度演化特点,并分析了隔热层对导热过程的影响以及隔热层导热性质不同情况下的温度分布特征.
Smoothed Particle Hydrodynamics( SPH) method is a recently-developed new numerical method,which has been successfully applied to solve a variety of engineering and physics problem. To revise particles approximation defects near the domain boundary and make up the deficiency of dealing with the boundary conditions in traditional SPH algorithm,Finite Difference Method( FDM) is coupled with the SPH algorithm,so that the approximation accuracy of a function can reach two order in the domain of interest and the accuracy of the calculation is improved; Then the second and third kind boundary condition of a fixed problem are handled based on the FDM algorithm,so that the calculation of complex boundary problems can be attributed to the solution of the first kind boundary problem. SPH-FDM coupling algorithm is used to calculate a series of heat conduction problems with different boundary conditions,which indicate that SPH-FDM algorithm can implement directly various boundary conditions and the calculated results has high precision and the solving process is reliable and effective by comparing with analytic solution. Finally,heat transmission problem of unsaturated soil medium is simulated using the coupling algorithm and the characteristic of temperature evolution with time is obtained,the effect of the insulator on heat conduction process is analyzed and temperature distribution characteristics with the insulator having different thermal conductivity is described.
出处
《应用基础与工程科学学报》
EI
CSCD
北大核心
2015年第5期952-965,共14页
Journal of Basic Science and Engineering
基金
高等学校博士学科点专项科研基金博导类资助课题(20130009110021)
中央高校基本科研业务费专项资金资助项目(2012YJS083)
国家自然科学基金项目(51279002)
关键词
光滑粒子法
耦合算法
边界修正
非饱和岩土介质
热能传导
smoothed particle hydrodynamics method
coupling algorithm
boundary correction
unsaturated soil medium
heat conduction
