动态大变形计算模拟的无网格强积分核函数

作为一种基于强函数积分形式的无网格计算方法,SPH（Smoothed Particle Hydrodynamics）方法在高能炸药爆炸、流体动力学及固体强冲击模拟计算中已经得到了广泛的应用.然而,目前该方法还存在许多问题,主要表现在拉伸不稳定性、零能量模式、边界条件实施困难、精度较差等,研究表明通过提高核函数的一致性可以使这些问题得到不同程度的改善.在RKPM（Reproducing Kernel Particle Method）方法基础上推导了高阶一致性核函数的公式,构造了适用于SPH方法的简化线性一致性核函数.通过算例证明了简化线性一致性核函数的可行性和优越性,即随着核函数一致性的提高,数值计算精度不断改善,最后对线性一致性核函数的非负特性进行了讨论.

The strong integrated kernel function in dynamic deformation simulations

As a strong integrated function of the true meshless method, the SPH （Smoothed Particle Hydrodynamics） method has been received relatively extensive application in the field of explosion, fluid dynamics and high velocity impact simulations. However, there are still some difficulties handicapping the realization of its full potential. It has been reported that the difficulties can be partially resolved by improving the consistency of SPH kernel function. Based on the RKPM （Reproducing Kernel Particle Method）, the formulations of high-order consistency kernel function are derived and a simplified linear consistent kernel function is proposed for the 3D SPH simulation. Through several numerical simulations, the accuracy is shown to be improved with the increase of degree of the consistency. The numerical convergence, computational efficiency and non-negative property of linear consistency kernel function are analyzed as well.