高速可压缩流的格子Boltzmann方法
Lattice Boltzmann Approach to High-Speed Compressible Flows
摘要：
提出了一种改进的格子Boltzmann模型。该模型由Kataoka和Tsutahara [Phys. Rev. E \textbf{69}，056702（2004）]的离散速度模型和适当的有限差分格式以及附加的耗散项组成。通过引入耗散项，可以灵活地选择模型中的参数，从而满足冯·诺依曼稳定性条件。分析了各种模型参数对数值稳定性的影响，并给出了一些参数的参考值。新方案适用于马赫数高达30（或更高）的亚音速和超音速流动，这是由著名的基准测试验证。对压力和密度比值很高（$1000:1$）的Riemann问题的模拟也显示出良好的精度和稳定性。规则和双马赫激波反射的成功恢复显示了格子Boltzmann模型在非平衡过程是内在的流体系统中的潜在应用。新的稳定性方案可以很容易地推广到其他格子玻尔兹曼模型。
英文摘要：
We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara [Phys. Rev. E \textbf{69}, 056702 (2004)] and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios ($1000:1$) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.
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