A Consistent Gas-kinetic Scheme Study Based On Boltzmann Equation For Continuous And Rarefied Gas Flows Numerical Simulation

Rare?ed Gas Dynamics is the important foundation of Aeronautics and Aerospace science.Meantime Boltzmann equation is located in the central point of Rare?ed Gas Dynamics.But Boltzmann equation is a very complicated integral and di?erential equation.It is impossible to obtain its solution accurately in mathematics,so it is necessary to use computational mathematics of theory and method for numerical simulation.However traditionally based on continuum hypothesis of Navier-Stokes equations in simulating rare?ed gas do a lot of limitations,so that base on the molecular thermal motion and statistical mechanics of Rare?ed Gas Dynamics is receiving more and more attention by scientists.With discretized partial velocity space,a multi-scale uni?ed gas-kinetic scheme based on Rare?ed Gas Dynamics of theory and Boltzmann-BGK model for entire Knudsen number ?ows is constructed.Within a time step the current scheme couples closely the evolution of macroscopic conservation variables with the evolution of microscopic gas distribution function.In comparison with LBM and other methods the advantage of this method is the un-splitting treatment of the particle transport and collision.Theoretically,once the physical process of particle transport and collision is modeled statistically by the kinetic dynamic equation,the transport and collision become a integrated process in space and time,and the numerical computation should be done consistently.Therefore numerically simulated time step can be more than the particle collision time and it become possible to simulate high Reynolds number and Mach number ?ows.In addition,due to its multi-scale character of the scheme,the corresponding heat ?ux can be modi?ed according to any realistic Prandtl number.The present paper has mainly three aspect works as follows:First of all,the Boltzmann equation including the internal variables is deduced;The relative theories of aerodynamics and rari?ed gas dynamics are summarized.Second,reconstruction accuracy of distribution function around interface ?ux is improved from two order to three order;Meantime interface ?ux is reconstructed by Hermite-Newton method,and the present paper has achieved one dimension reconstruction and two dimension reconstruction.At the end of this paper,a couple of classic tests are simulated to validate the scheme at the end of the present article and the results are satis?ed.