Finite difference solution of nonlinear model equations for rarified gas using discrete velocity ordinate method

Considering the general nonlinear Boltzmann equations uniform algorithm has been developed to simulate rarified flows at a wide Knudsen number range numerically. The collision term is approximated by BGK model and Shakov model, and two bi-velocity non-dimensionalized reduced distribution functions are introduced. The single tri-velocity model equation is transformed into a bi-velocity differential equation system through integrating weightedly the non-dimensionalized model equation about the third component of molecule velocity. The discrete velocity ordinate method associated with Gauss-Hermite quadrature and orthogonal polynomial quadrature is used to eliminate dependency of the reduced model equations on continuous molecule velocity space, then a set of hyperbolic conservative discrete equations with source terms are obtained from phase space to physical space, and a finite difference method related to a second-order upwind TVD scheme is selected to solve them both explicitly and implicitly. A two- dimensional supersonic Ar-gas flow around a cylinder is computed to show the effectivity of algorithm. Moreover, numerical results of two wall reflection models of gas molecules, namely diffuse reflection model and specular reflection model, are compared and analyzed.