Smoothed particle hydrodynamics stability analysis
Smoothed particle hydrodynamics stability analysis
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DOI：
10.1006/jcph.1995.1010
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发表时间：
1995
影响因子：
4.1
通讯作者：
J. Swegle;D. Hicks;S. Attaway
中科院分区：
文献类型：
--
作者：
J. Swegle;D. Hicks;S. Attaway
摘要 SPH（平滑粒子流体动力学）是一种无网格拉格朗日技术，作为目前用于分析大变形事件的数值技术的可能替代方案，颇具吸引力。最近使用三次 B 样条核对标准 SPH 方法进行的测试表明，拉伸状态可能存在不稳定，尽管在压缩过程中没有观察到此类困难。对 SPH 算法进行了冯·诺依曼稳定性分析，根据应力状态和核函数的二阶导数确定了稳定性或不稳定的标准。分析解释了该方法在拉伸中不稳定而在压缩中明显稳定的观察结果，但表明可以构造在拉伸中稳定而在压缩中不稳定的核函数。表明这种不稳定性是由本构关系与核函数之间的相互作用产生的具有负模量（虚声速）的有效应力引起的，而不是由数值时间积分算法引起的。也就是说，有效应力的变化会放大而不是减少应变的扰动。分析和稳定性标准提供了消除不稳定性的可能方法的见解。
Abstract SPH (smoothed particle hydrodynamics) is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze large deformation events. Recent tests of the standard SPH method using the cubic B-spline kernel indicated the possibility of an instability in the tensile regime, even though no such difficulties were observed in compression. A von Neumann stability analysis of the SPH algorithm has been carried out which identifies the criterion for stability or instability in terms of the stress state and the second derivative of the kernel function. The analysis explains the observation that the method is unstable in tension while apparently stable in compression but shows that it is possible to construct kernel functions which are stable in tension and unstable in compression. The instability is shown to result from an effective stress with a negative modulus (imaginary sound speed) being produced by the interaction between the constitutive relation and the kernel function and is not caused by the numerical time integration algorithm. That is, changes in the effective stress act to amplify, rather than reduce, perturbations in the strain. The analysis and the stability criterion provide insight into possible methods for removing the instability.