SPH方法核近似形式改进及算法研究  

IMPROVEMENT OF KERNEL APPROXIMATION FORM AND ALGORITHM RESEARCH OF SPH METHOD

作　　者：郑雄波 赵杰[1] 刘晓曦 何轩 姜劲[3] Zheng Xiongbo;Zhao Jie;Liu Xiaoxi;He Xuan;Jiang Jin(College of Mathematical Sciences,Harbin Engineering University,Harbin 150001,China;Southern Marine Science and Engineering Guangdong Laboratory,zhuhai 519000,China;Jinling Institute of Technology,Nanjing 211112,China)

机构地区：[1]哈尔滨工程大学数学科学学院,哈尔滨150001 [2]南方海洋科学与工程广东省实验室,珠海519000 [3]金陵科技学院,南京211112

出　　处：《数值计算与计算机应用》2023年第2期150-165,共16页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(52071094,52171261)资助。

摘　　要：光滑粒子流体动力学(Smoothed Particle Hydrodynamics,SPH)方法是一种无网格拉格朗日粒子法,目前在流体力学领域以及大变形和冲击载荷等问题的模拟方面具有广泛的应用,众多学者在SPH算法方面开展了大量的研究,以提高SPH算法的计算速度和精度.针对现有SPH方法在边界附近粒子近似精度下降的问题,本文在CSPH方法和MSPH方法基础上提出了一种改进的核近似形式,在求解场函数、一阶导数近似值以及二阶导数近似值过程中,对含二阶导数项的方程进行优化,减少了二阶导数项近似值的求解个数,相比MSPH方法减少了计算量.此外,本文基于改进的SPH算法,建立了二维数值波浪水槽模拟推板造波,通过数值模拟造波将SPH算法生成的波浪参数与理论值进行对比,验证了改进的SPH方法在波浪生成和传播上具有较好的模拟效果,为后续研究内波、畸形波以及非线性波相互作用提供了算法研究基础.Smoothed Particle Hydrodynamics(SPH)method is a meshless Lagrangian particle method,which is widely used in the field of fluid mechanics and the simulation of large deformation and impact load.Many scholars have done a lot of research on SPH algorithm to improve the calculation speed and accuracy of SPH algorithm.To solve the problem that the accuracy of particle approximation near the boundary of the existing SPH method decreases,this paper proposes an improved kernel approximation based on CSPH method and MSPH method.In the process of solving the field function,the first derivative approximation and the second derivative approximation,the equation with the second derivative term is optimized,which reduces the number of solutions of the second derivative approximation,and reduces the amount of calculation compared with MSPH method.In addition,based on the improved SPH algorithm,this paper established a two-dimensional numerical wave flume to simulate push-plate wave-making,and compared the wave parameters generated by SPH algorithm with the theoretical values through numerical simulation wave-making,which verified that the improved SPH method had a good simulation effect on wave generation and propagation,and provided an algorithm research foundation for the follow-up study of internal wave,freak wave and nonlinear wave interaction.

关 键 词：光滑粒子流体动力学 核近似 推板造波 数值水槽 

分 类 号：O35[理学—流体力学]