We consider a kinetic description of a multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are defined by a variational procedure \cite{arXiv:2101.09047}. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function, mimicking the Lagrange functional that appears in the theoretical derivation. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method, and illustrate its usefulness and effectiveness with numerical examples.
翻译:我们考虑对一种与Bhatnagar-Gross-Krook(BGK)碰撞操作员模拟的多物种气体混合物的动能描述,其中碰撞频率不仅在时间和空间上不同,而且与微粒速度也不同。在这个模型中,标准BGK操作员通常使用的Maxwellians通常被这种目标功能的概括化所取代,这种功能的定义是变式程序\cite{arXiv:2101.09047}。在本文中,我们提出了一个模拟该模型的数字方法,它使用隐含的(IMEX)方法来尽量减少某种潜在功能,模拟理论衍生中出现的Lagrange功能。我们表明,保有质量、总动力和总能量以及分配功能的假设性等理论性特性通过数字方法得以保留,并以数字实例来说明其效用和有效性。