Adaptive Total Lagrangian Eulerian SPH for high-velocity impacts
Adaptive Total Lagrangian Eulerian SPH for high-velocity impacts
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DOI：
10.1016/j.ijmecsci.2020.106108
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发表时间：
2021-02
影响因子：
7.3
通讯作者：
J. Young;F. Teixeira-Dias;A. Azevedo;F. Mill
中科院分区：
文献类型：
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作者：
J. Young;F. Teixeira-Dias;A. Azevedo;F. Mill
本文提出了一种新的光滑粒子流体动力学（SPH）方法的总拉格朗日和欧拉公式之间的耦合。它是这样实现的，总拉格朗日公式可以自适应转换为欧拉公式（在这项工作中称为AdapTLE），并适用于高速冲击问题。新的耦合利用混合内核和梯度校正方案，这是为了提高一致性和守恒动量。此外，对称项，这是经常发现在SPH，包括在守恒方程的推导，以减少所需的计算量。人工粘性的一种新的实现建议的总拉格朗日公式，它利用内核梯度在未变形的状态，因此不需要邻居列表进行更新。这种形式的人工粘性可以应用到一个奇异的全拉格朗日公式或耦合。数值例子，包括补丁测试，和二维和三维的高速碰撞问题进行了模拟，以评估这种新的耦合方法，并证明AdapTLE的好处，这被发现产生上级的结果，无论是总拉格朗日或欧拉制定独立。这是由于保留了全拉格朗日公式，直到严重变形需要转换为欧拉公式，这大大减少了后者的拉伸不稳定性的影响。
This paper presents a novel coupling between the Total Lagrangian and Eulerian formulations of the Smooth Particle Hydrodynamics (SPH) method. It is implemented such that a Total Lagrangian formulation can adaptively convert to an Eulerian formulation (referred to as AdapTLE in this work) and applied to high-velocity impact problems. The novel coupling makes use of the mixed kernel-and-gradient correction scheme, which is applied in order to improve consistency and conserve momentum. Additionally, the symmetrical terms, which are often found in SPH, are included in the derivation of the conservation equations to reduce the number of calculations required. A novel implementation of artificial viscosity is suggested for the Total Lagrangian formulation, which makes use of the kernel gradient in the undeformed state and therefore does not require neighbour lists to be updated. This form of artificial viscosity can be applied to a singularly Total Lagrangian formulation or a coupled one. Numerical examples including a patch test, and two-dimensional and three-dimensional high-velocity impact problems were simulated to evaluate this novel coupling method and demonstrate the benefits of AdapTLE, which was found to produce superior results to either a Total Lagrangian or Eulerian formulation independently. This was due to the retention of a Total Lagrangian formulation until severe distortions required the conversion to an Eulerian formulation, which significantly reduced the effect of the tensile instability in the latter.