Kinetics Format In Many Media Flow Of Gas And The Application Of Two Phase Flow Numerical Method

Numerical simulations for compressible multi-component flow and two-phase flow have been significant issues in computational fluid dynamics which have been applied in many areas. In recent years, the gas kinetic schemes have been developed systematically and have attracted much attention.The gas kinetic scheme is based on the BGK model which is the approxima-tion of Boltzmann equation. There is no need for us to construct Riemarm solver. In this paper, it is because of the advantages of the gas kinetic schemes that the gas kinetic scheme for the multi-component flow and Baer-Nunziato two-phase flow will be presented.In recent years, some gas-kinetic schemes for multicomponent flow have been presented. Based on the two-species BGK model, numerical scheme will be pre-sented. Different from the conventional BGK model, it takes the collisions both with particles of their species and the other species into consideration. No doubt that it will contain more physical information. Based on the Chapmann-Enskog expansion, the corresponding macroscopic equations could be derived from the two-species BGK model. To deal with the relaxation terms in the macroscopic equations, the method of operator splitting is applied. Integral solutions of the kinetic equations are used to construct the numerical fluxes at the cell interface in the framework of finite volume method. From the numerical results, spurious oscillations in the pressure and velocity counter are observed at the interface. Based on the interface model, we will analyze the reason of spurious oscillations.In the section of two-phase flow, we will take the Baer-Nunziato(BN) two-phase flow model into account. Because of the non-conservative product, there were many difficulties in development of the mathematical theory and numerical methods. Numerical methods for the BN two-phase flow model have attracted much attention in recent years. We will present a new gas kinetic scheme for the Baer-Nunziato two-phase flow model containing non-conservative terms. In the view of microscopic aspect, a BGK model containing external term which matches with the BN model is constructed. In this model, the non-conservative terms are considered as the external term in the BGK model. Based on the integral solution of the generalized BGK model, we construct the distribution functions at the cell interface. It could be observed that the non-conservative term not only play a role of source terms, but also bring the effect on the distribution function at the cell interface. Compared with exact Riemann solution and approximate Riemann solver, in our method, not only the complex iterative process of exact solutions is avoided, but also the non-conservative terms included in the equation can be handled well. And the over-diffusivity in the KFVS scheme which is based on the collisionless model is reduced in our gas kinetic scheme.It could be observed that we only consider the collisions with particles of their own phases in our BGK scheme for the BN model. By making use of the two-species BGK model and the BGK model containing external force, we could obtain a two-phase BGK model which not only contains the external force, but also takes the collisions both with particles of the other phase into consideration. Based on the Chapmann-Enskog expansion, a modified Bear-Nunziato two-phase model could be derived. A gas kinetic scheme is proposed based on the two-phase BGK model and modified Bear-Nunziato two-phase model. However, it is because of the lack of theoretical analysis for these models, more work is still left to be finished in the future.