Abstract: To investigate effect of rotational degree of freedom on gas flows covering various flow regimes,Boltzmann-Rykov model is studied and reduced velocity distribution functions are introduced with quadrature to rotational degree of freedom of molecular velocity distribution function.A single gas-kinetic model equation is translated into simultaneous equations of three reduced velocity distribution functions at discrete velocity ordinate points with discrete velocity ordinate method and numerical integration technique.One-and two-dimensional Boltzmann-Rykov model equations for diatomic gases are computed with finite-difference method of computational fluid dynamics.One-dimensional shock-tube and the two-dimensional flow past erect plate are analyzed in the whole range of Knudsen numbers.Reliability of gas-kinetic unified algorithm(GKUA) is validated in solving one-and two-dimensional flows from free molecular flow to continuum regimes.It is indicated that the gas rarefaction degree and molecular inner degree of freedom affect flow field greatly.And rarefied gas flows with high Knudsen numbers take serious non-equilibrium effect.

Key words: rotational degree of freedom, Boltzmann-Rykov model equation, shock-tube problem, erect plate flow, gas-kinetic unified algorithm