A fast iterative discrete velocity method for ternary gas mixtures flowing through long tubes

An accelerated discrete velocity method is presented for flows of three-component gas mixtures through long tubes. The gas is modeled by the McCormack linearized kinetic equation. Two diffusion equations are derived from the kinetic one. These equations are solved during the kinetic iteration by a linear algebraic approach. Test simulations are performed for flows of He-Ar-Xe mixture driven by pressure or temperature gradients in a wide range of the gas rarefaction. The accelerated method requires fewer number of iterations and smaller computational times than the non-accelerated one in the early transition, slip and near-hydrodynamic domains. The efficiency of the accelerated scheme compared to the standard one increases with increasing rarefaction parameter. The computational performance in terms of the iteration criterion is also analyzed. In typical simulations, the convergent results can be reached in approximately less than two minutes by using the new method in a wide range of the gas rarefaction on a present-day computer.