Corrected ALE-ISPH with novel Neumann boundary condition and density-based particle shifting technique
Corrected ALE-ISPH with novel Neumann boundary condition and density-based particle shifting technique
复制标题
DOI：
10.1016/j.jcpx.2023.100125
复制
发表时间：
2023-03
期刊：
影响因子：
--
通讯作者：
D. Morikawa;Kumpei Tsuji;M. Asai
中科院分区：
文献类型：
--
作者：
D. Morikawa;Kumpei Tsuji;M. Asai
众所周知，在光滑粒子流体力学（SPH）界，梯度和拉普拉斯算子的校正有可能以牺牲计算稳定性为代价，大幅提高方法的精度。本文提出了在任意拉格朗日欧拉不可压缩SPH （ALE-ISPH）方法的所有导数算子中稳定实现这种修正，以及直接应用于速度的新型诺伊曼边界条件（BC）（与传统的BCs（其中约束应用于加速度）相反）。这样，水和壁面颗粒的压力同时求解，得到了一个同时服从非侵透BC和无散度的压力场。此外，为了稳定该方法，我们开发了一种新的基于密度的颗粒移动技术（PST），专门用于处理不可压缩流体。在此公式中，数值密度作为最关键的约束变量之一。因此，所提出的基于密度的PST可以在整个模拟过程中保持流体的总体体积。此外，它还提供了数值稳定性，因为它可以防止颗粒聚集，并导致流体域的各向同性组成。首先，我们用新颖的Neumann BC验证了提出的修正公式，分别模拟了静水压力和泊泽努伊流，用于非穿透和非滑移条件。然后，我们用旋转方形补丁问题测试了提出的基于密度的PST，结果与先前的研究相当。最后，通过一个高动态问题——溃坝障碍试验，验证了所提方法的有效性。
It is well-known in the Smoothed Particle Hydrodynamics (SPH) community that correction in the gradient and Laplacian operators have the potential to drastically increase the accuracy of the method at the expense of computational stability. This paper proposes a stable implementation of such corrections in all derivative operators to the Arbitrary Lagrangian Eulerian incompressible SPH (ALE-ISPH) method, in addition to a novel Neumann boundary condition (BC) applied directly on the velocity (as opposed to traditional BCs where the constraint is applied on the acceleration). In this way, the pressure is solved for both water and wall particles simultaneously, leading to a pressure field that obeys non-penetration BC and divergence-free at the same time. Furthermore, to stabilize the method, we have developed a novel density-based particle shifting technique (PST), specifically designed to deal with incompressible fluids. In this formulation, the numerical density is given as one of the most critical constraint variables. As a result, the proposed density-based PST can maintain the fluid's overall volume for the whole simulation. In addition, it also provides numerical stability as it prevents particle clustering and leads the fluid domain to an isotropic composition. First, we verified the proposed corrected formulation with the novel Neumann BC for both non-penetration and non-slip conditions with the simulation of hydrostatic pressure and Poisenuille flow, respectively. Then, we tested the proposed density-based PST with the rotating square patch problem with results comparable to previous studies. Lastly, we verified the proposed method for the dam break with an obstacle test, a highly dynamic problem.