光滑粒子流体动力学法拉伸不稳定性改进研究

Improvement of tensile instability in smoothed particle hydrodynamics

摘要:

针对光滑粒子流体动力学(SPH)法在涉及材料强度的问题中存在着拉伸不稳定性,提出了一种改进拉伸不稳定性的连续型人工力,给出了其应用条件,并建立了该人工力的张量形式.通过在消除压缩不稳定性的人工粘性力的基础上叠加抗拉伸不稳定的人工力,建立了统一形式的人工力.通过两个算例的计算及比较,表明该人工力的计算结果振荡小并且接近有限元法的计算结果,优于其它形式的人工力.该人工力使SPH法的拉伸不稳定性得到了更好的改善.

Abstract:

To solve the problem that tensile instability may occur in adopting Smoothed Particle Hydrodynamics(SPH) in the cases involved in material strength,an artificial stress of continuum type was presented to improve the tensile instability.The condition of application of the artificial stress was given and the tensor form of the stress was set up.The unification form of artificial stress was established through combining the artificial viscosity stress that eliminates compressive instability and the artificial stress that resists tensile instability.Two examples were calculated and the results were compared.It is indicated that better results can be obtained by using the artificial stress presented than those of other forms.The results have less vibration and approach those of Finite Element Method,which proves that the artificial stress presented can improve the tensile instability in SPH.