Research On Two-Dimensional Numerical Simulation Of Shallow-Water Flows And Its Application

The phenomenons involved in flow problems are immediate research focuses in hydrodynamic field recently, such as offshore tidal, estuarine tidal bore, and dam-breaking. The particularity of this issue is that water flows driven by the gravity approximately along the horizontal direction, and physical quantities distribute discontinuously in the flow field which contains the shock wave. Navier-Stokes equations is an admittedly physically-based fluid dynamics model, which couldn’t answer the questions above yet, due to practical flow problems usually have wide computation domains and complex boundary conditions that influence the flow state and can’t be taken adequate care for. So Reynolds equations was born, according to Reynolds-average method. Based on the assumption of horizontal movement, two-dimensional shallow water equations which describes the questions above clearly could be deduced by averaging the various terms in Reynolds equations along the vertical direction.The numerical simulation technology breaking through the traditional restrictions has become one of powerful tools in science research, with the rapid development of modern computer. So that numerical solutions for two-dimensional shallow water equations are emerging in endlessly. Based on previous studies, this text has summarized and developed a complete set of numerical calculation model for two-dimensional shallow water flow, In process of model building, the control equations is discreted by the finite volume method using unstructured triangle grids. The core problem of solving the discrete equations which is the evaluation of numerical flux has been also identified. In order to solve this problem, Godunov method has been used to convert which to one-dimensional Riemannian problem in the local coordinate system based on the assumption of discontinuity. Therefore, numerical flux in the direction normal to and across each side of elements is obtained by a first-order upwind scheme based on Roe’s approximate Riemann solver. Source terms are discreted separately by the sloping plane model and A weighted average implicit difference scheme to alleviate stabilities and compatibilities of the scheme. In addition, generality of the numerical calculation process has been taken into account when the key questions associated with numerical calculation are disposed, which include setting initial and boundary conditions, distinguishing wetting and drying boundaries, and so on. Virtual element method and the characteristic scheme are both used to get the issue of the elements on the border of computation domain which have only physical quantities on one side over, and the matter of wetting and drying boundaries are worked out by modifying landform of dry nodes to transform the wetting and drying elements into wetting elements.Dam-breaking water flow is one kind of typically discontinuous and unsteady flow, which could detect advantages and disadvantages of the scheme. Numerical simulations of several dam-breaking problems are carried out making use of the model having been established. The results show that ability and definition of the scheme in capturing discontinuity solution is high, and the outcomes of processing wetting and drying boundaries are also well-pleasing, meeting the requirements of accuracy and resolution ratio. So that it can be applied to solve practical flow problems. At the last part, numerical simulations of two engineering problems are carried out to turn out that the model could precisely and efficiently do with the practical flow problems, the results of which have been compared with the measured data.