A discrete unified gas-kinetic scheme for multi-species rarefied flows

Abstract

In this work, a discrete unified gas kinetic scheme (DUGKS) is developed for multi-species flow in all flow regimes based on the Andries-Aoki-Perthame (AAP) kinetic model. Although the species collision operator in the AAP model conserves fully the mass, momentum, and energy for the mixture, it does not conserve the momentum and energy for each species due to the inter-species collisions. In this work, the species collision operator is decomposed into two parts, one part is fully conservative for the species and the other represents the excess part. With this decomposition, the kinetic equation is solved following the Strang-splitting procedure, in which the excess part of the collision operator is treated as a source, while the kinetic equation with the species conservative part is solved by the standard DUGKS. Particularly, the time integration of the source term is realized by either explicit or implicit Euler scheme. By this means, it is easy to extend the scheme to gas mixtures composed of Maxwell or hard-sphere molecules, while the previous DUGKS [Y. Zhang et al., Phys. Rev. E 97, 053306 (2018)] of binary gases was only designed for Maxwell molecules. Several tests are performed to valid the scheme, including the shock structure and plane Couette flow. Excellent agreement is observed between the solutions of the present method and the previous DUGKS and the unified gas kinetic scheme. The results also show that the present DUGKS with implicit source discretization is preferable for gas mixture flow problems involving different flow regimes.