The Finite Volume And Kinetic Flux Vector Splitting Method Based On The Boltzmann Equation

Flood movement causes a serious damage to the survival and development of humans. An effective and accurate forecasts and predictions are not only an important item to attract people's attention, but also have a great theoretical value and practical significance. The research in flood routing is based on flood wave's movement rule, that is flood wave's propagation, smoothing and transfiguration rule. It is just to offer scientific decision—making gist for exploring water resource. In recent years, computational fluid dynamics, as a subject, has been a powerful tool for flood and developed rapidly. A precise scheme of the one-dimensional shallow water equations was studied in this paper according to the previous studies and the flux vector splitting method, which can deal with some complicated problems.Firstly, we outlined the significance, the existing status quo and some of the important algorithms about the computational fluid dynamics, additional a brief account of the Roe's operator method of Riemann problems. Secondly, we make a detailed statement about the development, the principles and the arithmetic of the KFVS. Thirdly, a new finite volume flux vector splitting has been proposed and used to the solutions of one-dimensional shallow water equations with source terms until the achievement of previous studies has been introduced. The new algorithm is based on the Boltzmann micro-fluid dynamics equations and considered the transform of the speeds and directions of the micro-particles which caused by the source terms, as well as a appropriate restrictions function will be chosen automatically according to the different wave during the numerical separating. Using this algorithm, it can improve the precision greatly and catch the shock effective.Finally, we proposed a moving boundary KFVS algorithm based on the Boltzmann equation. It restructured the boundary micro-particle distribution function by the wet and dry neighbored-cell distribution functions, and then transferred the affections to the macro parameters. This algorithm can reflect the physical nature of water campaign laws differ from the traditional moving boundaries of the law.The corresponding numerical examples are given. The experimental results show that the above algorithm is accurate and applicable to solve a series of flood problems. It also has a certain value and the practical application and theoretical significance.