【摘要】 在非平衡气体动力论和稀薄气体动力学的理论研究中,发展了模方程法[1—4]。本文将逆碰撞积分写成f_z~n乘以对应的速度多项式为通项的级数形式,导出了一种新的非平衡气体动力论模方程,并应用该方程研究了冲激波结构问题,取得了良好结果。更多还原

【Abstract】 Motion of non-equilibrium gas may be described in terms of kinetic theory with Boltzmann equation several authors have developed model equations for approximate solution of the Boltzmann equation.The present paper gives another improved new model equation as an approximation to the Boltzmann equation. The principal idea on which the present model equation is based may be explained as follows, the nonlinear inverse collision integral term must be expressed by nonlinear terms. In the present paper, the inverse collision integral is expressed by a power series in terms of local equilibrium velocity distribution fe. It is required that the moments of the model collision integral approach thoses of the Boltzmann collision integral. We have used the Maxwell molecular model, which is a special case of the inverse power law model. Then we can express the moments of Boltzmann collision integral with moments of the distribution function.So, our model equation of kinetic theory of the nonequilibrium gas may be written as:where :where :f -- velocity distribution function ; n -- number density of molecule ; c -- velocity vector of molecule ; t -- time ; Te -- local equilibrium temperature ; fe -- the local equilibrium distribution function, corresponding to Te ; q -- heat flux vetor C --thermal or random molecular velocity.It may be shown, that the Maxwellian velocity distribution function is the solution of present model equation. The collision invariants of present equation are the same as Boltzmann equation.Using well-known Chapmann-Enskog method, we have obtained the perturbation solution of the present model equation, from which we obtain Pr =2/3. The result is agreement with experimental results for monoatomic gas. The structure of normal shock wave is considered using the present model equation. Numerical results agree with experimental results.更多还原