二阶核近似有限粒子方法的改进  

Modified finite particle method with second kernel approximation

作　　者：李建成[1] 袁德奎[1,2] 陶建华[1,3] 

机构地区：[1]天津大学机械工程学院,天津300072 [2]四川大学水力学与山区河流开发保护国家重点实验室,成都610065 [3]天津大学环境科学与工程学院,天津300072

出　　处：《水动力学研究与进展（A辑）》2013年第3期260-273,共14页Chinese Journal of Hydrodynamics

基　　金：天津市自然科学基金重点项目(11JCZDJC24200);新世纪优秀人才支持计划(NCET-12-0406)~~

摘　　要：该文对基于相容性核近似方法的二阶核近似光滑粒子流体动力学方法(K2_SPH方法)中函数及导数的核近似估计方法进行了改进,提出了一种改进的二阶核近似有限粒子方法(SK2_FPM方法)。以一维情况为例对SPH方法、K2_SPH方法和SK2_FPM方法的核近似精度进行了理论推导和比较分析,并用Poiseuille流动、Couette流动以及一阶线性驻波问题三个经典算例对模型进行了检验。结果表明,随着核近似精度的改进,SK2_FPM方法较传统SPH方法和K2_SPH方法在计算精度和稳定性上都有一定程度的提高。According to the kernel approximation for the function as well as the derivatives in K2_SPH, which is based on the particle consistency method, a modified finite particle method is introduced, namely a simplified second kernel approximation finite particle method （SK2_FPM）. Taking one dimensional case as an example, the accuracy characteristics of kernel approximation for SPH, K2SPH and SK2_FPM are theoretically derived and taken a comparative analysis among them. Then SK2_FPM is verified with three classic examples, which are Poiseuille flow, Couette flow and linear Standing Wave problem. With the improvement of kernel approximation, the results of SK2_FPM show that, higher accuracy and more stability compared with traditional SPH and K2_SPH to some extent.

关 键 词：无网格方法 光滑粒子流体动力学(SPH) SK2_FPM K2_SPH 

分 类 号：TV131.2[水利工程—水力学及河流动力学]