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Lattice Boltzmann method with selective viscosity filter

机译：带有选择性粘度过滤器的Lattice Boltzmann方法

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For high-Reynolds number flows, the lattice Boltzmann method suffers from numerical instabilities that can induce local blowup of the computation. The von Neumann stability analysis applied to the LBE-BGK and LBE-MRT models shows that numerical instabilities occur in the high wavenumber range and are due to the interplay between acoustic modes and some other modes. As it is done in the LBE-MRT model, an increase of the bulk viscosity is an efficient way of damping spurious oscillations. However, this stabilization method induces an over-damping of acoustic waves. Some selective spatial filters can be used in order to eliminate the spurious small spatial scales without affecting the large scale physical modes. Three different lattice Boltzmann algorithms based on filtering step are proposed: the fully filtered LBE, the LBE with filtered macroscopic quantities and the LBE with filtered collision operator. The behavior of several explicit filter stencils is studied in the Fourier space. For a given filter stencil, the filtered collision operator approach leads to the highest cut-off wavenumber. In this case, the theoretical wavenumber-dependent viscosity is ν (k) = c_s~2 (τ / [1 - σ f (k)] - 1 / 2) where f (k) is the filter shape and σ the filter strength. Under-resolved simulations (high Reynolds number) are performed on the case of the doubly periodic shear layers. The performance of the three filtered LBE is found to be the same as the MRT model for stability control. Propagation of acoustic plane waves is also simulated with the three filtering algorithms. The measured dissipation of acoustic wave compares well with the theoretical results.
机译：对于高雷诺数流，晶格玻尔兹曼法存在数值不稳定性的问题，可能导致局部计算爆炸。应用于LBE-BGK和LBE-MRT模型的冯·诺依曼稳定性分析表明，数值不稳定性发生在高波数范围内，这是由于声学模式与其他模式之间的相互作用所致。正如在LBE-MRT模型中所做的那样，提高体积黏度是一种抑制寄生振荡的有效方法。但是，这种稳定方法会引起声波的过度阻尼。可以使用一些选择性的空间滤波器以消除虚假的小空间尺度，而不影响大尺度的物理模式。提出了三种基于滤波步骤的格子Boltzmann算法：完全滤波的LBE，具有滤波后的宏观量的LBE和具有滤波后的碰撞算子的LBE。在傅立叶空间中研究了几个显式过滤器模具的行为。对于给定的过滤器模板，过滤后的碰撞算子方法会导致最高的截止波数。在这种情况下，与波数有关的理论粘度为ν（k）= c_s〜2（τ/ [1-σf（k）]-1/2），其中f（k）是过滤器形状，σ是过滤器强度。对双周期剪切层的情况进行了欠解析模拟（高雷诺数）。发现三个滤波后的LBE的性能与用于稳定性控制的MRT模型相同。声平面波的传播也用三种滤波算法进行了模拟。测得的声波耗散与理论结果相吻合。

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