Discrete Unified Gas-kinetic Scheme For Incompressible Flows And Its Applications

Research of the incompressible flows has an important significance in practical appli-cations, which is involved in the most of the energy, the chemical industry and the environ-ment fields, such as the development of the storage and oil displacement of CO2, the clean combustion, the emission and control of the absorbed particle and so on. The mesoscopic method has been demonstrated to be an effective approach to the incompressible flows and has achieved significant success in theory and applications. However, it also suffers from some problems. Recently, the discrete unified gas kinetic scheme (DUGKS) has been de-veloped and can overcome these problems theoretically, but hasn't been demonstrated by numerical experiments. In addition, the DUGKS for incompressible flows hasn't been thor-oughly studied as a new proposed method, and is also limited to isothermal flows. Therefore, in the present thesis, we conduct the following research work:Firstly, the numerical errors and asymptotic preserving property of the DUGKS are an-alyzed, and the features of the DUGKS modeling are compared with the unified gas-kinetic scheme (UGKS) and the finite-volume lattice Boltzmann equation (LBE) methods. The re-sults show that the coupled transport and collision stages guarantees that the DUGKS has low numerical dissipation and nice Asymptotic Preserving (AP) property; the comparison results also show its superiority to the previous mesoscopic method.Secondly, the DUGKS is compared with the standard LBE method for the incompress-ible flows in terms of accuracy, numerical stability and computational efficiency. The results show that the DUGKS and LBE methods have the same accuracy, but the numerical stability of the former is much better than the latter, and the efficiency of the former can be signifi-cantly improved by the implementation of the non-uniform mesh.Thirdly, direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulent (DHIT) flow is conducted by the DUGKS. The kinetic energy and its dissipation rate, energy and its dissipation rate spectrum, flatness and skewness are studied by compar-ing with those from the LBE and the pseudo spectral methods. The results show that the DUGKS is a reliable kinetic method for DNS of DHIT, and this work is the basis of our further study of the wall-bounded turbulent flows.Finally, the coupled discrete unified gas-kinetic scheme (CDUGKS) and kinetic bound-ary conditions are developed to extend the DUGKS to thermal incompressible flows. The results show that the CDUGKS has a better numerical stability and is much easier to be implemented on the uniform mesh than the previous mesoscopic method. In addition, we applied the CDUGKS to study the 2D and 3D natural convection flow with the Rayleigh number up to 1010. It should be noted that the flow characteristics and the heat transfer of the 3D natural convection with such high Rayleigh number is first systematically studied. It is found that there is an exponential relation between the Rayleigh number and the Nusselt number, and our predictions agree well with the results from the pseudo spectral method and the experiments.In summary, in this thesis, we study and analyze the performance of the DUGKS for incompressible flows, and apply the DUGKS and CDUGKS to the turbulence flow and high Rayleigh number natural convection flow, respectively. It is demonstrated that the DUGKS has overcome the shortcomings of the numerical stability and implementation of the non-uniform mesh in the LBE method. This work plays a basis role in the future related work.