修正SPH方法在冲击波中的应用

Shock wave analysis with a corrective smoothed particle hydrodynamics method

SPH方法以核近似作为基础,受到核近似连续性原理的限制,在求解域中粒子必须是满足均匀分布的,这对SPH方法的应用也非常不利;同时,由于紧支域边界截断误差的存在,使得结果在边界上的误差常常比较大.对上述问题,在传统SPH方法的基础上,对核近似离散过程进行了修正,并引入黎曼解构成了修正的SPH方法,即CSPH和GSPH方.应用3种SPH方法对一维冲击管问题及一维爆轰波问题进行了对比研究.从分析结果可知在CSPH方法的基础上改进的GSPH方法有效地改善了传统SPH方法在非连续冲击波问题中的计算精度、相容性等问题,大大提高了传统SPH方法捕获间断信息的精度.

The smoothed particle hydrodynamics（SPH） method,based on kernel approximation,is limited by the consistency principle of kernel approximations.Particles must be uniformly distributed,and since they are generally not,the application of the SPH method may not produce favorable results.At the same time,errors will be very large at the boundary because of truncation errors at the boundary of the domain compactly supported.To resolve the problems mentioned above,the process of kernel approximation was modified,based on the traditional SPH method.The Riemann solution was added,making it a corrective smoothed particle method,or CSPH/GSPH.A comparative study of the effects of a detonation process in a one-dimensional shock tube was done using this method.From the results it could be seen that improved GSPH on the basis of the CSPH method effectively resolved the traditional SPH method＇s weaknesses,such as discontinuity impairing accuracy,compatibility,and so on.It also greatly enhanced accuracy in capturing intermittent information.