An extension of Godunov SPH II: Application to elastic dynamics
An extension of Godunov SPH II: Application to elastic dynamics
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DOI：
10.1016/j.jcp.2016.12.026
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发表时间：
2016-05
期刊：
影响因子：
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通讯作者：
K. Sugiura;S. Inutsuka
中科院分区：
文献类型：
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作者：
K. Sugiura;S. Inutsuka
Goddom光滑粒子流体动力学（Goddom SPH）方法是一种利用黎曼解算器的计算流体动力学方法，在空间上达到二阶精度。在本文中，我们将Goddom SPH方法扩展到弹性动力学中，通过引入偏应力张量来表示剪切变形或各向异性压缩的应力。类似于制定原来的Goddom SPH方法，我们制定的运动方程，能量方程，和偏应力张量的时间演化方程，使所得的离散系统在空间上达到二阶精度。标准的SPH方法容易受到张力不稳定性的影响，导致粒子的非物理聚集，特别是在张力主导的区域。我们发现，拉伸不稳定性可以抑制通过选择适当的插值密度分布的运动方程的Goddom SPH方法，即使在弹性动力学的情况下。弹性动力学的几个测试计算进行，本方法的准确性和通用性。
Godunov Smoothed Particle Hydrodynamics (Godunov SPH) method is a computational fluid dynamics method that utilizes a Riemann solver and achieves the second-order accuracy in space. In this paper, we extend the Godunov SPH method to elastic dynamics by incorporating deviatoric stress tensor that represents the stress for shear deformation or anisotropic compression. Analogously to the formulation of the original Godunov SPH method, we formulate the equation of motion, the equation of energy, and the time evolution equation of deviatoric stress tensor so that the resulting discretized system achieves the second-order accuracy in space. The standard SPH method tends to suffer from the tensile instability that results in unphysical clustering of particles especially in tension-dominated region. We find that the tensile instability can be suppressed by selecting appropriate interpolation for density distribution in the equation of motion for the Godunov SPH method even in the case of elastic dynamics. Several test calculations for elastic dynamics are performed, and the accuracy and versatility of the present method are shown.