相对论性麦克斯韦粒子混合气体的梯度矩方法
Grad's moment method for relativistic gas mixtures of Maxwellian particles
摘要：
本文在玻尔兹曼方程的框架内，用格拉德矩法分析了相对论性混合气体。相对论混合物的$r$成分的分布函数的时刻：粒子四流，能量动量张量和三阶矩张量的特点。利用Eckart分解，引入与混合物的速度、温度、粒子数密度、扩散通量、非平衡压力、热通量和压力偏量张量有关的$13r+1$标量场，得到了Grad分布函数。对于组分静止质量相差不大的混合物，用Grad分布函数确定三阶张量及其产生项，使其服从$13r+1$标量场方程组.通过限制到一个二元混合物的特点是由六个字段的部分粒子数密度，四速度和温度，其余21个标量方程用于确定本构方程的非平衡压力，扩散通量，压力偏张量和热通量。因此，Navier-Stokes和广义的傅立叶和Fick定律得到的体积和剪切粘度，导热系数，扩散，热扩散和扩散热的传输系数的确定。进一步，以强迫波和自由波的形式给出了二元混合物的相对论性场方程的解。在低频限制的情况下，相速度和衰减系数确定为强迫波。在小波数限制的情况下，它示出，存在四个纵向本征模，其中两个对应于传播的声音模式和两个与非传播扩散模式。
英文摘要：
Mixtures of relativistic gases are analyzed within the framework of Boltzmann equation by using Grad's moment method. A relativistic mixture of $r$ constituent is characterized by the moments of the distribution function: particle four-flows, energy-momentum tensors and third-order moment tensors. By using Eckart's decomposition and introducing $13r+1$ scalar fields -- related with the four-velocity, temperature of the mixture, particle number densities, diffusion fluxes, non-equilibrium pressures, heat fluxes and pressure deviator tensors -- Grad's distribution functions are obtained. Grad's distribution functions are used to determine the third-order tensors and their production terms for mixtures whose constituent's rest masses are not too disparate, so that it follows a system of $13r+1$ scalar field equations. By restricting to a binary mixture characterized by the six fields of partial particle number densities, four-velocity and temperature, the remainder 21 scalar equations are used to determine the constitutive equations for the non-equilibrium pressures, diffusion fluxes, pressure deviator tensors and heat fluxes. Hence the Navier-Stokes and generalized Fourier and Fick laws are obtained and the transport coefficients of bulk and shear viscosities, thermal conductivity, diffusion, thermal-diffusion and diffusion-thermal are determined. Furthermore, solutions of the relativistic field equations for the binary mixture are obtained in form of forced and free waves. In the low frequency limiting case the phase velocity and the attenuation coefficient are determined for forced waves. In the small wavenumber limiting case it is shown that there exist four longitudinal eigenmodes, two of them corresponding to propagating sound modes and two associated with non-propagating diffusive modes.
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