SPH compressible turbulence
SPH compressible turbulence
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DOI：
10.1046/j.1365-8711.2002.05678.x
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发表时间：
2002-04
影响因子：
4.8
通讯作者：
J. Monaghan
中科院分区：
文献类型：
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作者：
J. Monaghan
在这篇论文中，霍尔姆和他的同事们设计了一个光滑粒子流体动力学（SPH）版本的阿尔法湍流模型，该模型是为可压缩流制定的，其分辨率随空间和时间的变化而变化。alpha模型涉及两个速度场。一个速度场是由动量方程得到的，另一个是通过平均这个速度场得到的，就像SPH的XSPH版本一样。粒子（流体单元）以平均速度移动。与连续体模型类似，我们得到了一个粒子拉格朗日量，由此可以推导出SPH方程。该系统满足离散开尔文循环定理，与没有速度平均的情况下得到的定理相同。此外，能量、线动量和角动量守恒。我们证明了SPH方程的连续统等效与连续统α模型是相同的，并且我们推测它们将具有连续统模型相同的理想特征，包括即使在耗散为零的情况下，高波数模式中的能量也会减少。抛开湍流建模的问题，SPH alpha模型是XSPH算法的强大扩展，它减少了短长度尺度上的无序性，并保留了运动的常数。SPH alpha模型很容易实现。
In this paper a smoothed particle hydrodynamics (SPH) version of the alpha turbulence model devised by Holm and his colleagues is formulated for compressible flow with a resolution that varies in space and time. The alpha model involves two velocity fields. One velocity field is obtained from the momentum equation, the other by averaging this velocity field as in the version of SPH called XSPH. The particles (fluid elements) are moved with the averaged velocity. In analogy to the continuum alpha model we obtain a particle Lagrangian from which the SPH alpha equations can be derived. The system satisfies a discrete Kelvin circulation theorem identical to that obtained with no velocity averaging. In addition, the energy, linear and angular momentum are conserved. We show that the continuum equivalent of the SPH equations are identical to the continuum alpha model, and we conjecture that they will have the same desirable features of the continuum model including the reduction of energy in the high-wavenumber modes even when the dissipation is zero. Regardless of issues concerning turbulence modelling, the SPH alpha model is a powerful extension of the XSPH algorithm, which reduces disorder at short length-scales and retains the constants of the motion. The SPH alpha model is simple to implement.