A multi-degree-of-freedom gas kinetic multi-prediction implicit scheme

Abstract

A multi-scale implicit multi-degree-of-freedom (MDOF) kinetic model with molecular translational, rotational and vibrational effects is presented. The evolution and exchange of energy among translational, rotational and vibrational degrees of freedom are demonstrated by three coupled relaxation processes. An orthogonal polynomial system is used to involve heat-transfer and viscosity properties in construction of a sequence of objective distribution functions at various relaxation stages. Based on finite volume discrete velocity method framework, the asymptotic preserving discrete unified gas-kinetic scheme (DUGKS) flux is adopted to preserve particle motion information. A second-order prediction scheme based on the Navier-Stokes flux is constructed to predict macroscopic variables from macroscopic residuals for implicit DUGKS iteration, which contains a multiple prediction methodology. The current MDOF kinetic model provides a concrete insight into energy exchange between the rotational and vibrational degrees of freedom during molecular inelastic collisions. The accurate prediction procedure significantly accelerates convergence. Several numerical test cases, including rarefied gas flow in lid-driven cavity, variable specific heat ratio shock structure, hypersonic circular cylinder flows at different Knudsen and Mach numbers, and hypersonic flat plate flow, are performed to validate the accuracy and efficiency of present model. All numerical results of the present method agreed well with those of the reference data. A 2∼3 orders-of-magnitude improvements in computational efficiency of the multi-scale implicit method are achieved compared with the explicit method. It demonstrated that the present method is a promising scheme considering vibration-rotation-translation energy exchange of poly-atomic molecules for the fast simulation of multi-scale flows from low-speed incompressible flow to hypersonic flow, from continuum to rarefied regime.