可压缩流体的多重弛豫时间格子Boltzmann模型
Multiple-relaxation-time lattice Boltzmann model for compressible fluids
摘要：
本文提出了一个能量守恒的多重弛豫时间有限差分格子Boltzmann模型。该模型基于16离散速度模型。首先在力矩空间中计算碰撞步长，然后将其映射回速度空间。根据群表示理论构造了矩空间和相应的变换矩阵。根据Chapman-Enskog展开法恢复可压缩纳维-斯托克斯方程的需要，选取了非守恒矩平衡。数值试验表明，该模型能较好地模拟强激波作用下的可压缩流动。所使用的基准测试包括（i）激波管，例如Sod、Lax、Sjogreen、Colella爆炸波和两个强激波的碰撞，（ii）规则激波和马赫激波反射，以及（iii）圆柱形气泡问题上的激波反应。新模型适用于低速和高速可压缩流。它包含了更多的物理信息，并具有更好的数值稳定性和精度比它的单弛豫时间版本。
英文摘要：
We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. This model is based on a 16-discrete-velocity model. The collision step is first calculated in the moment space and then mapped back to the velocity space. The moment space and corresponding transformation matrix are constructed according to the group representation theory. Equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapman-Enskog expansion. Numerical experiments showed that compressible flows with strong shocks can be well simulated by the present model. The used benchmark tests include (i) shock tubes, such as the Sod, Lax, Sjogreen, Colella explosion wave and collision of two strong shocks, (ii) regular and Mach shock reflections, and (iii) shock wave reaction on cylindrical bubble problems. The new model works for both low and high speeds compressible flows. It contains more physical information and has better numerical stability and accuracy than its single-relaxation-time version.
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