Accelerated discrete velocity method for axial-symmetric flows of gaseous mixtures as defined by the McCormack kinetic model

An accelerated discrete velocity method is presented to calculate the steady axial-symmetric flows of gaseous mixtures defined by the McCormack kinetic model. The scheme is formulated in cylindrical coordinates. Diffusion equations for the macroscopic velocity and the heat-flow are derived on the basis of the projected McCormack equations. The solutions of the kinetic equations are carried out iteratively by using the discrete velocity method. The diffusion equations are also solved in each stage of the iteration in order to accelerate the scheme. Pressure driven flows of He/Xe and Ne/Ar mixtures through a cylindrical tube are simulated in order to study the computational performance of the approach. It is shown that the required number of iterations and the computational times are significantly reduced at intermediate and large values of the rarefaction parameter by using the accelerated method. In the hydrodynamic limit, the flow rates of the components converge to the corresponding slip flow results. Flows driven by mole fraction gradient are also successfully simulated. Typical velocity and heat-flow profiles for pressure driven flow of He/Xe mixture are shown and commented on.