Study Of Discrete Unified Gas-kinetic Scheme For Non-equilibrium Flow Of Diatomic Gases

Multi-scale flows of rarefied gas appear in many engineering applications such as near space vehicles,spacecraft and vacuum technology.Due to the strong non-equilibrium effect in multi-scale flows in rarefied environment,high-speed and high-temperature regions will appear in the flow field and temperature field,respectively.Using numerical methods to efficiently simulate multi-scale flows plays an important role in engineering applications.In recent years,a series of asymptotic preserving schemes have been developed,which can be used to simulate multi-scale flow problems.Among them,the Discrete Unified Gas Kinetic Scheme(DUGKS)couples the collision and migration processes of particles when reconstructing the interface flux,which can accurately describe flow problems from continuum to free-molecule regimes.And the DUGKS has been extended to the fields of heat transfer and radiation because of its relative simplicity.In order to apply DUGKS to the multi-scale flows of real gas efficiently,it is still necessary to extend the method to problems of polyatomic gases with internal degrees of freedom,and further improve the computational efficiency of the method.In this thesis a DUGKS is proposed for multiscale flows of diatomic gases,and a solver is then developed,based on which a number of typical non-equilibrium flows are studied.The main contributions are summarized as follows:(1)A DUGKS is constructed in which the rotational freedom of gas molecules are taken into account.The scheme is then validated by simulating the shock structure,supersonic flow over a plate,and the supersonic flow around a cylinder.Furthermore,a solver based on the open source code dugks Foam is developed,which can be applied to flows with complex geometrics.(2)A DUGKS with rigorous conservation is developed,and the conservation properties is verified by simulating the shock structure problem.Further,an implementation of the Gauss-Hermite quadrature formula is proposed,such that it can be used for high-Mach number flows in the conserved DUGKS,which significantly reduces the computational costs.(3)The transient multi-scale flow of a diatomic gas between two square cavities connected with a thin tube is studied by the developed DUGKS and the Open FOAM solver.Four stages are identified and the flow characteristics are analyzed,where the effects of pressure ratio,tube length,and the volume of low-pressure cavity are studied.