论文标题
关于Navier Stokes方程近似的单分布晶格Boltzmann方案
On single distribution lattice Boltzmann schemes for the approximation of Navier Stokes equations
论文作者
论文摘要
在这项贡献中，我们研究了多分辨率晶格玻尔兹曼方案的形式能力近似具有单个颗粒分布的等温和热压缩Navier Stokes方程。更确切地说，我们总共考虑了12个经典的正方形晶格Boltzmann方案，并具有规定的保守和未保守的力矩。问题是要确定未经保护的矩的平衡函数的代数表达以及与每个方案相关的弛豫参数。我们比较了二维示例的流体方程和泰勒膨胀方法的结果，最大速度和三维方案的二维示例最多具有33个速度。在某些情况下，不可能完全拟合物理模型。对于几个示例，我们调整了Navier Stokes方程，并提出了平衡的非平地表达式。
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 physical model. For several examples, we adjust the Navier Stokes equations and propose nontrivial expressions for the equilibria.
