时间-空间双重自适应光滑粒子流体动力学在冲击碰撞大变形问题中的应用

Development of time-space adaptive SPH for large deformation and impact

为提高光滑粒子流体动力学法(SPH)的计算效率,有学者提出了一种粒子能随时间自适应分裂及合并的空间自适应SPH算法(ASPH),并得到了广泛应用.然而现有ASPH法的自适应分裂模式在模拟大变形及碰撞问题时会引起粒子紊乱,且分裂后需采用较小的时间步长.本文开发了一种基于相对位矢和速度插值的自适应分裂模式,并结合Runge-Kutta Chebyshev(RKC)法在时域上进行自适应时间积分,最终提出了一种时间-空间双重自适应的SPH法(T-S ASPH).该算法不仅能够消除现有ASPH在模拟大变形与碰撞问题时的粒子紊乱现象,提高计算精度,还能提高算法的计算效率及时间积分的精度.经典SPH、现有ASPH以及本文所开发的T-S ASPH法对典型问题的模拟结果表明,与其他两种方法相比,T-S ASPH算法在模拟大变形及碰撞问题时,其计算精度更高,具有更高的效率及稳定性,并且其收敛阶数也更高.

A spatially adaptive smoothed particle hydrodynamics(ASPH)method,where the particles can split and merge according to the adaptive criteria,was developed to improve the computational efficiency of the classical smoothed particle hydrodynamics(SPH)method.Recently,the ASPH algorithm has been widely applied to solve complex problems in mechanics.However,the splitting pattern in the current ASPH algorithm may lead to particle disorder when simulating large deformation and impact problems,and a smaller time step should be performed after particle splitting.An adaptive splitting pattern that is based on a relative position vector and velocity interpolation is introduced in this study.Subsequently,this numerical method is combined with the Runge-Kutta Chebyshev method to achieve adaptive time integration.Thus,the time-space adaptive smoothed particle hydrodynamics method(T-S ASPH)is proposed in this study.This algorithm can increase the computational accuracy by eliminating the particle disorder when simulating the large deformation and impact problems while improving the computational efficiency and time integration accuracy.Typical examples are simulated by the classical SPH,current ASPH and developed T-S ASPH methods.The results indicate that,compared with the other two methods,the proposed T-S ASPH method exhibits higher accuracy,efficiency,stability,and order of convergence for the large deformation and impact problems.