标题： NRxx方法用于多原子气体 显示英文标题

标题： The NRxx Method for Polyatomic Gases

摘要： 本文中，我们提出了一种数值正则化矩方法，以求解具有ES-BGK碰撞项的玻尔兹曼方程，从而模拟多原子气体流动。该方法是对文献[9]中提出的方法在多原子情况下的扩展，该方法在文献[8]中被简称为NRxx方法。基于麦克斯韦分布的形式，内部能量参数的拉盖尔多项式用于分布函数的级数展开。我们为多原子气体开发了NRxx方法所需的所有关键技术，包括在数值通量计算中使用的高效投影算法、基于麦克斯韦迭代的正则化和量级方法，以及为了方便数值实现的正则化项线性化。同时，提出了针对ES-BGK碰撞项的时间特殊积分器。给出了从Knudsen数0.05到5的激波管模拟，以证明我们方法的有效性。此外，我们的数值实验还包括从1.53到6.1马赫数的氮气激波结构问题。 显示英文摘要

摘要： In this paper, we propose a numerical regularized moment method to solve the Boltzmann equation with ES-BGK collision term to simulate polyatomic gas flows. This method is an extension to the polyatomic case of the method proposed in [9], which is abbreviated as the NRxx method in [8]. Based on the form of the Maxwellian, the Laguerre polynomials of the internal energy parameter are used in the series expansion of the distribution function. We develop for polyatomic gases all the essential techniques needed in the NRxx method, including the efficient projection algorithm used in the numerical flux calculation, the regularization based on the Maxwellian iteration and the order of magnitude method, and the linearization of the regularization term for convenient numerical implementation. Meanwhile, the particular integrator in time for the ES-BGK collision term is put forward. The shock tube simulations with Knudsen numbers from 0.05 up to 5 are presented to demonstrate the validity of our method. Moreover, the nitrogen shock structure problem is included in our numerical experiments for Mach numbers from 1.53 to 6.1.