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A local Lagrangian gradient smoothing method for fluids and fluid-like solids: A novel particle-like method

机译：流体和类流体固体的局部拉格朗日梯度平滑方法：一种新颖的类粒子方法

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摘要

The Lagrangian Gradient Smoothing Method (L-GSM) proposed in our earlier work overcomes effectively the 'tensile instability' problem inherently existed in the widely used smoothed particle hydrodynamics (SPH) method. However, the employment of background grid in L-GSM for the construction of gradient smoothing domains leads some drawbacks to the L-GSM framework: low computational efficiency, complex implementation procedure and technical challenges for parallel computing algorithm development. Accordingly, this study proposes a novel particle-like method, termed as local L-GSM (LL-GSM), through constructing gradient smoothing domains locally for LL-GSM particles. The present LL-GSM consists of three unique ingredients: (1) Only locally constructed gradient smoothing domains are used; (2) an efficient localized neighbor-searching algorithm is developed for the search of supporting particles; (3) a simple and effective free surface technique is adopted for accurate application of free surface effect. The accuracy, stability and efficiency of the newly proposed LL-GSM framework are then investigated comprehensively by conducting thorough theoretical and numerical analyses. At last, benchmark problems including two incompressible flows and two free surface flows are used to verify the capability of LL-GSM in handling large deformation of fluids and fluid-like solids. The LL-GSM results are evaluated carefully by comparing with experimental results, theoretical solutions, and numerical solutions. Results comparison demonstrates that the proposed LL-GSM method can give very accurate numerical solutions in all these problems with a much better computational efficiency and easier implementation. It is also evidenced that, same to L-GSM, the LL-GSM is free from the 'tensile instability' issue.
机译：我们早期工作中提出的拉格朗日梯度平滑法（L-GSM）有效地克服了广泛使用的平滑粒子流体动力学（SPH）方法固有的“拉伸不稳定性”问题。然而，在L-GSM中使用背景网格来构建梯度平滑域会给L-GSM框架带来一些弊端：低计算效率，复杂的实现过程以及并行计算算法开发的技术挑战。因此，这项研究提出了一种新颖的类粒子方法，称为局部L-GSM（LL-GSM），方法是为LL-GSM粒子局部构建梯度平滑域。当前的LL-GSM由三个独特的成分组成：（1）仅使用局部构造的梯度平滑域； （2）开发了一种有效的局部邻居搜索算法来搜索支持粒子； （3）采用简单有效的自由表面技术来精确施加自由表面效应。然后，通过进行详尽的理论和数值分析，对新提出的LL-GSM框架的准确性，稳定性和效率进行了全面研究。最后，基准问题包括两个不可压缩流动和两个自由表面流动被用来验证LL-GSM处理流体和类流体固体大变形的能力。通过与实验结果，理论解和数值解进行比较，仔细评估了LL-GSM结果。结果比较表明，所提出的LL-GSM方法能够在所有这些问题上给出非常精确的数值解，并且具有更高的计算效率和更容易的实现。也有证据表明，与L-GSM一样，LL-GSM也没有“拉力不稳定”的问题。

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