We give an explicit description of the spectral closure for the three-dimensional linear Boltzmann-BGK equation in terms of the macroscopic fields, density, flow velocity and temperature. This results in a new linear fluid dynamics model which is valid for any relaxation time, thus providing an optimal hydrodynamic model for rarefied gas flow over a large range of Knudsen numbers. The non-local exact fluid dynamics equations are compared to the Euler, Navier–Stokes and Burnett equations. Our results are based on a detailed spectral analysis of the linearized Boltzmann-BGK operator together with a suitable choice of spectral projection.

我们根据宏观场、密度、流速和温度对三维线性 Boltzmann-BGK 方程的光谱闭合进行了明确描述。这产生了一个新的线性流体动力学模型，该模型适用于任何弛豫时间，从而为大范围克努森数的稀薄气体流动提供了最佳流体动力学模型。将非局部精确流体动力学方程与 Euler、Navier-Stokes 和 Burnett 方程进行了比较。我们的结果基于线性化 Boltzmann-BGK 算子的详细谱分析以及合适的谱投影选择。