A Consistent Second Order ISPH for Free Surface Flow
A Consistent Second Order ISPH for Free Surface Flow
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DOI：
10.1016/j.compfluid.2024.106224
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发表时间：
2024-02
期刊：
影响因子：
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通讯作者：
Ningbo Zhang;S. Yan;Q. Ma;Abbas Khayyer;Xiaohu Guo;Xing Zheng
中科院分区：
文献类型：
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作者：
Ningbo Zhang;S. Yan;Q. Ma;Abbas Khayyer;Xiaohu Guo;Xing Zheng
不可压缩平滑粒子流体动力学 (ISPH) 现在是一种流行的数值方法，用于模拟自由表面流，特别是破碎波和剧烈的波结构相互作用。 ISPH 需要投影方法，从而求解压力泊松方程 (PPE)。尽管用于离散 PPE 中拉普拉斯算子的数值方案的准确性和收敛性对于确保 PPE 的满意解至关重要，但 ISPH 的整体性能也受到其他关键数值实现的影响，包括（1）粘性项的估计； (2)速度散度的计算； (3) PPE 边界条件的离散化； (4)压力梯度的评估。在我们之前的论文[29]中，采用二次半解析有限差分插值方案（QSFDI）来离散拉普拉斯算子，该方案在三阶导数处具有领先的截断误差。本文将采用QSFDI，不仅可以离散拉普拉斯算子，还可以近似粘性项、速度散度、边界条件和压力梯度。新制定的一致二阶 ISPH 的性能通过包括振荡液滴、波传播和液体晃动在内的各种情况进行评估。结果不仅证明了在有限条件范围内的二阶收敛性和更高的计算效率，即需要更少的计算时间来达到相同的精度，而且还显示出比本研究中考虑的其他 ISPH 模型更好的质量/能量守恒特性和再现平滑压力场的能力。
The Incompressible Smoothed Particle Hydrodynamics (ISPH) is now a popular numerical method for modelling free surface flows, in particular the breaking waves and violent wave-structures interaction. The ISPH requires the projection approach, leading to solving a pressure Poisson's equation (PPE). Although the accuracy and convergence of the numerical scheme to discretise the Laplacian operator involved in PPE is critical for securing a satisfactory solution of the PPE, the overall performance of the ISPH is also influenced by other key numerical implementations, including (1) estimation of the viscous terms; (2) calculation of the velocity divergence; (3) discretisation of the boundary conditions for the PPE; and (4) evaluation of the pressure gradient. In our previous paper [29], the quadratic semi-analytical finite difference interpolation scheme (QSFDI), which has a leading truncation error at third order derivatives, has been adopted to discretise the Laplacian operator. In this paper, the QSFDI will be adopted, not only for discretising the Laplacian operator, but also for approximating viscous terms, velocity divergence, boundary conditions and pressure gradient. The performance of the newly formulated consistent second order ISPH is assessed by various cases including the oscillating liquid drop, the wave propagation, and the liquid sloshing. The results do not only demonstrate a second order convergence over a limited range of conditions and a higher computational efficiency, i.e., requiring less computational time to achieve the same accuracy, but also show a better mass/energy conservation property and capacity of reproducing a smooth pressure field, than other ISPH models considered in this study.