Multiscale Modeling &Simulation, Volume 18, Issue 2, Page 970-998, January 2020.
This work is devoted to the numerical simulation of the Bhatnagar--Gross--Krook (BGK) equation for two species in the fluid limit using a particle method. Thus, we are interested in a gas mixture consisting of two species without chemical reactions assuming that the number of particles of each species remains constant. We consider the kinetic two species model proposed by Klingenberg, Pirner, and Puppo in [Kinetic Rel. Models, 10 (2017), pp. 445--465], which separates the intra- and interspecies collisions. We want to study numerically the influence of the two relaxation terms, one corresponding to intraspecies and the other to interspecies collisions. For this, we use the method of micro-macro decomposition. First, we derive an equivalent model based on the micro-macro decomposition (see Bennoune, Lemou, and Mieussens [J. Comput. Phys., 227 (2008), pp. 3781--3803] and Crestetto, Crouseilles, and Lemou [Kinetic Rel. Models, 5 (2012), pp. 787--816]). The kinetic micro part is solved by a particle method, whereas the fluid macro part is discretized by a standard finite volume scheme. The main advantages of this approach are that (i) the noise inherent to the particle method is reduced compared to a standard (without micro-macro decomposition) particle method, and (ii) the computational cost of the method is reduced in the fluid limit since a small number of particles is then sufficient.

中文翻译：

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两组分气体混合物的动力学/流体微宏数值方案

多尺度建模与仿真，第18卷，第2期，第970-998页，2020年1月。
这项工作致力于使用粒子法对流体极限中两种物质的Bhatnagar-Gross-Krook（BGK）方程进行数值模拟。因此，我们对由两种没有化学反应的物质组成的气体混合物感兴趣，假设每种物质的颗粒数保持恒定。我们考虑由Klingenberg，Pirner和Puppo在[Kinetic Rel。模型，10（2017），第445--465页]，将种间和种间碰撞分开。我们想从数值上研究两个松弛项的影响，一个项对应于种内碰撞，另一个项对应于种间碰撞。为此，我们使用了微宏分解的方法。首先，我们基于微观宏分解得出等效模型（请参见Bennoune，Lemou和Mieussens [J. Comput。Phys。，227（2008），第3781--3803页]和Crestetto，Crouseilles和Lemou [运动版。范本，第5版（2012），第787--816页]。动力学微观部分通过粒子方法求解，而流体宏观部分通过标准有限体积方案离散化。这种方法的主要优点是：（i）与标准（无微宏分解）粒子方法相比，降低了粒子方法固有的噪声，并且（ii）在流体极限方面降低了该方法的计算成本因为少量的颗粒就足够了。