Compressible Non-conserved Two-phase Model Gks Study

For the demands of researching two-phase flow phenomenon such as deflagration-to-detonation transition in gas-permeable reactive granular materials, two-phase flow produced by the solid explosive detonation and so on, a non-conservative two-phase flow model was proposed by Baer and Nunziato. As the model well prescribes the function between two phases, it has become the research hot spot. In order to get higher order accuracy, traditional numerical algorithm needs to construct an exact Riemann solver or approximate Riemann solver in the calculation of initial-value problem. Thus, it is a huge computation load because of iterative progress. The situation is much worse when comes to two-phase flow calculation, as the best Riemann solver needs double iteration. In addition, the Baer-Nunziato equation is non-conservative, and none of the existing discretization method for the non-conservative terms is mature. The non-conservative terms cannot be treated as flux or common source terms. Therefore, the algorithm for two-phase flow with non-conservative terms is not only major front but also researching hot spot. This paper is for the purpose of constructing a GKS model. We prospect the same accuracy with schemes constructed by Riemann solver, but much less calculation loads.Firstly, we outlined the application, history and research methods of two-phase flow, and gave a simple introduction for GKS:history and the present situation. Then, we described the BN non-conservative two-phase flow model, its characteristic analysis and Riemann solver, and the unity of GKS method with the macroscopic Euler equation. After reviewing the Kinetic Vector Splitting Scheme, we proposed a gas-kinetic scheme for non-conservative two-phase flow and examined the unity between our scheme and Baer-Nunziato model.The key point of this paper is to construct a GKS model for BN non-conservative equation. Based on previous study, we proposed our GKS model and proved the unity with BN equation. Then we gave a detailed solution step of the new method as well as the numerical tests. The algorithm was based on the KFVS, and for its uniqueness, non-conservative terms were explicitly introduced into the evolution and construction of numerical fluxes. Thus non-conservation terms were discretized well. Comparing with traditional scheme, our method raised the computation speed enormously by avoiding approximate Riemann solver. Massive numerical tests suggested the accuracy and the robust of the new method and its widespread application prospect.