The linear form of the error propagation of SPH,which was obtained through perturbation method,has been employed to analyze the tensile instability in SPH.The sufficient condition for tensile instability,which was eve...The linear form of the error propagation of SPH,which was obtained through perturbation method,has been employed to analyze the tensile instability in SPH.The sufficient condition for tensile instability,which was ever presented by Swegle,could also be derived from the eigenvalues of the linear form.Hence,the eigenvalues correspondingly yielded a tensile stability criterion.The criterion confirmed the Swegle's statement that the tensile instability is induced by imaginary sound speed,and revealed the origins of imaginary sound speed and some details of CFL conditions.Moreover,a reasonable numerical sound speed,which accords with the one given by Monaghan through dimensional analysis,was also derived from the criterion.The kernel's spatial derivatives,which are only with respect to the distance between particles,were found it was not accurate if the spatial derivatives of smoothing lengths were not trifle.展开更多
基金Sponsored by the National Natural Science Foundation of China (Grant No. 10832007)
文摘The linear form of the error propagation of SPH,which was obtained through perturbation method,has been employed to analyze the tensile instability in SPH.The sufficient condition for tensile instability,which was ever presented by Swegle,could also be derived from the eigenvalues of the linear form.Hence,the eigenvalues correspondingly yielded a tensile stability criterion.The criterion confirmed the Swegle's statement that the tensile instability is induced by imaginary sound speed,and revealed the origins of imaginary sound speed and some details of CFL conditions.Moreover,a reasonable numerical sound speed,which accords with the one given by Monaghan through dimensional analysis,was also derived from the criterion.The kernel's spatial derivatives,which are only with respect to the distance between particles,were found it was not accurate if the spatial derivatives of smoothing lengths were not trifle.
