A comparative study of truly incompressible and weakly compressible SPH methods for free surface incompressible flows
A comparative study of truly incompressible and weakly compressible SPH methods for free surface incompressible flows
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DOI：
10.1002/fld.3824
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发表时间：
2013-11
影响因子：
1.8
通讯作者：
Z. Chen;Z. Zong;M. B. Liu;H. T. Li
中科院分区：
文献类型：
--
作者：
Z. Chen;Z. Zong;M. B. Liu;H. T. Li
本文比较分析了不可压缩SPH（ISPH）方法和改进的弱可压缩SPH（IWCSPH）方法在求解自由面不可压缩流问题中的性能。在这两种方法中，Navier-Stokes方程求解，没有使用人工粘性。本文提出的ISPH算法是基于经典的SPH投影法，对固体边界和自由曲面进行了一般处理。IWCSPH模型包括密度近似和固体边界处理（SBT）中的一些先进的校正算法。在密度近似中，移动最小二乘（MLS）方法被应用于每隔几步重新初始化密度，以获得更平滑和更稳定的压力场。本文提出了一种改进的耦合动态SBT算法，以获得稳定的固体壁面附近的压力值，从而减小固体边界可能带来的数值振荡。用ISPH和IWCSPH对静水压力基准试验、溃坝问题和液体晃动问题三个有代表性的算例进行了对比分析。结果表明，目前的IWCSPH是更有吸引力的比ISPH在模拟自由表面不可压缩流，因为它是更准确，更稳定的可比甚至更少的计算工作量。版权所有© 2013约翰威利父子有限公司.
In this paper, the performance of the incompressible SPH (ISPH) method and an improved weakly compressible SPH (IWCSPH) method for free surface incompressible flows are compared and analyzed. In both methods, the Navier–Stokes equations are solved, and no artificial viscosity is used. The ISPH algorithm in this paper is based on the classical SPH projection method with common treatments on solid boundaries and free surfaces. The IWCSPH model includes some advanced corrective algorithms in density approximation and solid boundary treatment (SBT). In density approximation, the moving least squares (MLS) approach is applied to re‐initialize density every several steps to obtain smoother and more stable pressure fields. An improved coupled dynamic SBT algorithm is implemented to obtain stable pressure values near solid wall areas and, thus, to minimize possible numerical oscillations brought in by the solid boundaries. Three representative numerical examples, including a benchmark test for hydrostatic pressure, a dam breaking problem and a liquid sloshing problem, are comparatively analyzed with ISPH and IWCSPH. It is demonstrated that the present IWCSPH is more attractive than ISPH in modeling free surface incompressible flows as it is more accurate and more stable with comparable or even less computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.