可压缩流动的极坐标格子Boltzmann模拟
Polar coordinate lattice Boltzmann modeling of compressible flows
摘要：
本文提出了一个极坐标格子Boltzmann动力学模型。给出了从离散分布函数恢复连续分布函数的方法。在该模型中，提出了一种类似于算子分裂但又不同于算子分裂的混合方案。对流项采用改进的Warming-Beam（MWB）格式求解，并在MWB格式中引入了合适的开关函数。目前的模型不仅适用于亚音速流动，而且适用于超音速流动。它是通过以下著名的基准测试进行验证和验证：（i）旋转流，（ii）稳定激波管问题，（iii）Richtmyer-Meshkov（RM）不稳定性，（iv）开尔文-亥姆霍兹不稳定性。作为应用，我们研究了两种特殊情况下系统在激波、稀疏波和物质界面三种界面附近的非平衡特性。在这两种情况中的一种情况下，材料界面初始扰动，从而发生RM不稳定性。研究发现，由于偏离热力学平衡，材料界面附近的宏观效应与机械界面附近的宏观效应有很大的不同。材料界面的初始扰动增强了不同自由度分子运动的耦合。激波附近偏离热力学平衡的幅度远大于稀疏波和材料界面附近。通过比较高阶矩的各个分量及其在平衡态下的值，可以定性地得出实际分布函数的主要行为。
英文摘要：
We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modifiedWarming-Beam (MWB) scheme.Within theMWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RMinstability occurs. It is found that themacroscopic effects due to deviating from thermodynamic equilibrium around thematerial interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function.
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