二维turbulence在无滑移方箱中衰减的光滑粒子流体动力学直接数值模拟
Direct Numerical Simulation of decaying two-dimensional turbulence in a no-slip square box using Smoothed Particle Hydrodynamics
摘要：
本文探讨了SPH方法在二维无滑移壁面区域衰减湍流直接数值模拟（DNS）中的应用。在这个有界域中，逆能量级联和由边界施加的净扭矩导致流体的自发旋转，导致填充域的大涡旋的典型结束状态。SPH模拟结果与发表的结果进行了比较，使用高精度的伪谱代码。的动能，拟能和平均涡波数相比，以及对伪谱的结果，作为流体的总角动量的演变。然而，虽然伪谱结果强调了无滑移边界作为流中长寿命相干涡发生器的重要性，但SPH结果中没有看到这种生成。在边界处产生的涡丝总是在从边界层分离后不久就被流动耗散掉。SPH结果的动能谱是使用SPH傅立叶变换计算的，该变换直接作用于无序粒子。系综动能谱在大部分惯性范围内显示出预期的k-3标度。然而，光谱在较小的长度尺度上变平（最初小于7.5个粒子间距，随着时间的推移尺寸不断增大），表明小尺度动能过剩。
英文摘要：
This paper explores the application of SPH to a Direct Numerical Simulation (DNS) of decaying turbulence in a two-dimensional no-slip wall-bounded domain. In this bounded domain, the inverse energy cascade, and a net torque exerted by the boundary, result in a spontaneous spin up of the fluid, leading to a typical end state of a large monopole vortex that fills the domain. The SPH simulations were compared against published results using a high accuracy pseudo-spectral code. Ensemble averages of the kinetic energy, enstrophy and average vortex wavenumber compared well against the pseudo-spectral results, as did the evolution of the total angular momentum of the fluid. However, while the pseudo-spectral results emphasised the importance of the no-slip boundaries as generators of long lived coherent vortices in the flow, no such generation was seen in the SPH results. Vorticity filaments produced at the boundary were always dissipated by the flow shortly after separating from the boundary layer. The kinetic energy spectrum of the SPH results was calculated using a SPH Fourier transform that operates directly on the disordered particles. The ensemble kinetic energy spectrum showed the expected k-3 scaling over most of the inertial range. However, the spectrum flattened at smaller length scales (initially less than 7.5 particle spacings and growing in size over time), indicating an excess of small-scale kinetic energy.
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