论文标题
具有速度依赖性碰撞频率的多物种BGK模型的数值方案
Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency
论文作者
论文摘要
我们考虑了以Bhatnagar-Gross-Krook（BGK）碰撞运算符建模的多物种气体混合物的动力学描述，其中碰撞频率不仅在时间和空间上变化，而且在微观速度上也有所不同。在此模型中，通常在标准BGK运算符中使用的麦克斯韦人被此类目标函数的概括所取代，这些函数由变量过程\ cite {arxiv：2101.09047}定义。在本文中，我们提出了一种模拟该模型的数值方法，该方法使用隐式解释（IMEX）方案来最大程度地减少某些潜在函数，从而模仿了理论派生中出现的Lagrange功能。我们表明，诸如质量保护，总动量和总能量以及分布函数的阳性之类的理论特性可以通过数值方法保留，并通过数值示例说明了其有用性和有效性。
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.
