In this contribution we study the formal ability of a multi-resolution-times lattice Boltzmann scheme to approximate isothermal and thermal compressible Navier Stokes equations with a single particle distribution. More precisely, we consider a total of 12 classical square lattice Boltzmann schemes with prescribed sets of conserved and nonconserved moments. The question is to determine the algebraic expressions of the equilibrium functions for the nonconserved moments and the relaxation parameters associated to each scheme. We compare the fluid equations and the result of the Taylor expansion method at second order accuracy for bidimensional examples with a maximum of 17 velocities and three-dimensional schemes with at most 33 velocities. In some cases, it is not possible to fit exactly the physicalmodel. For several examples, we adjust the Navier Stokes equations and propose nontrivial expressions for the equilibria.

翻译：本文研究了多分辨率时间格点玻尔兹曼格式在单一粒子分布下近似等温与可压缩热纳维-斯托克斯方程的形式能力。具体而言，我们考察了12种经典的方形格点玻尔兹曼格式，这些格式具有预设的守恒矩与非守恒矩集合。问题在于确定各方案中非守恒矩平衡函数的代数表达式以及对应的弛豫参数。我们通过二阶精度的泰勒展开方法，对比了最大速度数为17的二维示例与最大速度数为33的三维格式的流体方程。在某些情况下，无法精确拟合物理模型。针对多个示例，我们对纳维-斯托克斯方程进行了调整，并提出了平衡态的非平凡表达式。