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基于改进粒子移位技术的SPH与自由表面流模拟

SIMULATION OF FREE-SURFACE FLOWS USING SPH WITH AN IMPROVED PARTICLE SHIFTING TECHNOLOGY

  • 摘要: 光滑粒子流体动力学(Smoothed Particle Hydrodynamics, SPH)作为一种无网格的数值方法, 已被广泛应用于自由表面流动的模拟中. 在SPH的模拟中, 经常会遇到负压引起的张力不稳定性以及粒子分布不均问题, 这会导致自由表面附近产生非物理间隙, 从而影响计算的稳定性与精确性. 粒子位移技术(Particle Shifting Technology, PST)作为一种有效的改进方案被广泛引入, 但现 有的几种PST改进方案仍面临着计算复杂性较高和自由表面不光滑等问题. 为了解决这些问题, 文章在弱可压缩SPH的框架内, 提出了一种改进的粒子位移技术(NPST), 该方法在解决自由表面附近非物理间隙问题的同时, 通过控制自由表面粒子对自由表面附近粒子的影响来补全自由表面的缺失, 从而解决自由表面不规则问题. 为了验证了NPST的稳定性和有效性, 文章通过对数值造波、方形液滴旋转、液滴振荡三个经典自由表面流问题进行数值模拟. 结果表明, 这种改进的粒子位移技术不仅保留了传统PST的优良特性, 且算法简单更易于实现, 能够在一定程度上提高计算效率. 同时通过与IPST的结果进行对比分析, 进一步表明, NPST能够有效解决自由表面附近粒子分布不均匀的问题, 从而提升计算精度.

     

    Abstract: Smoothed Particle Hydrodynamics (SPH), as a meshless numerical method, has been widely used in the simulation of free-surface flows due to its inherent ability to deal with large deformations, topological variations, and free-surface fragmentation. In the numerical simulation of SPH, tension instability caused by negative pressure and uneven particle distribution are often encountered, which can lead to the creation of unphysical gaps near the free surface, thus affecting the stability and accuracy of the calculation. Particle Shifting Technology (PST) has been widely introduced as an effective improvement scheme to alleviate the above problems by redistributing particles and maintaining spatial homogeneity, but several existing PST improvement schemes still face problems such as high computational complexity and non-smooth free surface. In order to solve these problems, the article proposes an improved particle displacement technique (NPST) within the framework of weakly compressible SPH, based on the IPST proposed by Wang et al. The method solves the problem of non-physical gaps in the vicinity of the free surface while compensating for the lack of the free surface by controlling the effect of the free-surface particles on particles in the vicinity of the free surface to solve the problem of free-surface irregularity. In order to verify the stability and validity of the NPST, the article performs numerical simulations of three classical free-surface flow problems, namely, numerical wave-making, square droplet rotation, and droplet oscillation. The results show that this improved particle displacement technique not only retains the excellent characteristics of the traditional PST, but also the algorithm is simple and easier to implement, which can improve the computational efficiency to a certain extent. Meanwhile, by comparing and analyzing the results with those of IPST, it is further shown that NPST can effectively solve the problem of inhomogeneous distribution of particles near the free surface, thus improving the computational accuracy.

     

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