A Multi-Degree-Of-Freedom Gas Kinetic Multi-Prediction Implicit Scheme

A multi-scale implicit method for solving Boltzmann phenomenological model equation with translational, rotational and vibrational effects is presented. The correct ratio of thermal conductivity and viscosity are provided by introducing a orthogonal polynomials to construct a sequence of objective distribution functions. The energy transfer among translation, rotation and vibration degrees of freedom is demonstrated by three coupled relaxation processes. Based on finite volume discrete velocity method (DVM) framework, the asymptotic preserving (AP) discrete unified gas-kinetic scheme (DUGKS) flux is adopted to preserve particle motion information. A second-order prediction scheme based on the Navier-Stokes (NS) flux is constructed to predict macroscopic variables from macroscopic residuals for implicit DUGKS iteration, which contains a multiple prediction methodology. The current 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 variable specific heat ratio shock structure, hypersonic circular cylinder flows on different Knudsen and Mach numbers, and hypersonic flat plate flow, are performed to verify the accuracy and efficiency of present model. All numerical results of the present method are agreed well with those of the reference data. A $2 \sim 3$ orders-of-magnitude improvements in computational efficiency of the multi-scale implicit method is 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 the rarefied to the continuum regime