A unified gas-kinetic scheme for axisymmetric flow in all Knudsen number regimes

Abstract

Based on kinetic model equation, a unified gas-kinetic scheme for axisymmetric flow (UGKS-AS) is proposed in the whole flow regimes. The flux transport of UGKS-AS is based on a reduced gas distribution function of a time integral solution of the full 3D BGK model. In the cylindrical coordinate system, the local time evolution of convection and source terms for the macroscopic and microscopic flow variables is fully coupled with particle free transport and collisions. As a result, a multiple scale UGKS-AS is developed and used for the flow simulation from the free molecular transport to the Navier–Stokes solutions. In comparison with the full 3D UGKS method for axisymmetric flow, the present scheme is much more efficient and gives accurate solution in all flow regimes. Different from operator splitting methods with decoupled treatment of particle transport and collision, for the Navier–Stokes solution in the continuum regime the UGKS-AS doesn't have the constraint on the time step being less than the particle collision time. To further improve the efficiency of the scheme for steady state solution, an implicit UGKS-AS method is also developed. A large number of numerical tests for axisymmetric flow are conducted by the proposed explicit and implicit UGKS-AS, which include inner and outer, steady and unsteady, low and high speed flows. Some tests are very challenging due to the delicate capturing of very small flow variations. The good agreement among the solutions from the present scheme and other analytical, numerical, and experimental studies, validates the high accuracy and efficiency of the UGKS-AS for non-equilibrium flow simulation in all regimes.