Theoretical analysis on the applicability of traditional SPH method  

作　　者：ZHOU GuangZheng GE Wei LI JingHai 

机构地区：[1]State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences

出　　处：《Chinese Science Bulletin》2013年第24期2970-2978,共9页

基　　金：supported by the National Natural Science Foundation of China (21206167);the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA07080203)

摘　　要：As a fully Lagrangian, particle-based numerical method, the traditional smoothed particle hydrodynamics (SPH) generally suffers from the accuracy problem. To investigate the physical origins of this numerical error, the elastic effect between SPH particles is specifically identified by analogy with physical entities, and a unique non-dimensional number is proposed to evaluate the relative dominance of viscous to elastic effect. Through the simulation of two-dimensional Couette flow, the velocity profile and arrangement of particles are examined for various ratios of viscous to elastic effect. The effective viscosity of SPH particles decreases as this non-dimensional number increases, while the increase of particle number significantly reduces the effective viscosity only at lower ratio of viscous to elastic effect. The disparity among nominal viscous dissipation, total dissipation, and theoretical dissipation further confirms the presence of unphysical dissipation resulting from the elastic effect. In summary, due to the constraints from the Mach number and the ratio of viscous to elastic effect, there exists a critical Reynolds number below which the Newtonian behavior could be approximately obtained through suitable choice of model parameters.As a fully Lagrangian, particle-based numerical method, the traditional smoothed particle hydrodynamics （SPH） generally suffers from the accuracy problem. To investigate the physical origins of this numerical error, the elastic effect between SPH particles is specifically identified by analogy with physical entities, and a unique non-dimensional number is proposed to evaluate the relative dominance of viscous to elastic effect. Through the simulation of two-dimensional Couette flow, the velocity profile and ar- rangement of particles are examined for various ratios of viscous to elastic effect. The effective viscosity of SPH particles de- creases as this non-dimensional number increases, while the increase of particle number significantly reduces the effective viscos- ity only at lower ratio of viscous to elastic effect. The disparity among nominal viscous dissipation, total dissipation, and theoreti- cal dissipation further confirms the presence of unphysical dissipation resulting from the elastic effect. In summary, due to the constraints from the Mach number and the ratio of viscous to elastic effect, there exists a critical Reynolds number below which the Newtonian behavior could be approximately obtained through suitable choice of model parameters.

关 键 词：SPH方法 光滑粒子流体动力学 传统 适用性 COUETTE流 粘性耗散 弹性效应 无量纲数 

分 类 号：O35[理学—流体力学] O351.2[理学—力学]