The Unstructured 2D And 3D Shallow Water Model Study Based On Godunov And Semi-Lagrangian Method

Based on the finite volume framework and Roe type approximate Riemann solver, the one-and two-dimensional unstructured grid high-resolution model is presented with nonlinearshallow water equations with source terms. The three-dimensional unstructured baroclinicturbulence model with three-dimensional shallow water equations, transport equations and GLS(Generic Length Scale) turbulence equations is established by Semi-Lagrangian method.Firstly, based on the Roe type approximate Riemann solver, the one-dimensional model is presented for the shallow water equation with source terms. The source terms are decomposed in the characteristic directions, which keep the flux balance at the interface and protected the scheme harmonious. The MUSCL (Monotonic Upstream Schemes for Conservation Laws) and two-step Runge-Kutta are used for higher order scheme. Several numerical models are used for verifying the model.Secondly, the high resolution and high order two-dimensional model with unstructured grid is developed. The source terms are also decomposed in the characteristic directions, and the limiter water depth method is used for the wetting and drying interface, which improved the useful of the model. The model is demonstrated on several numerical models, including the standard rectangle dam break problem, supercritical channel flow problems, steady and unsteady flows over a channel with three mounds problem and non-symmetric dam break problem. At last the model is used to simulate the flood routing of PanTouPao detention basin and the flow in the PengLaiTan river segment, which verify the applicability, reliability of the model.Thirdly, the unstructured turbulence baroclinic numerical model for three-dimensional unsteady free surface turbulence flow and mass (salt and temperature) convection is developed by using the GLS turbulence model and three-dimensional shallow water equations. The semi-implicit method is used for the continuity equation and vertical diffusion terms of momentum equations and the Semi-Lagrangian method are used for the convection and horizontal diffusion terms, which keep this model "unconditional stability". The different turbulence closed models can be used while the suitable parameters are used for GLS modeling,so it is easy for studying the turbulence model. The model has several ability: efficient, unstructured, "unconditional stability", so it could be used for the simulation of large-scale flow. Fourthly, the three-dimensional model is applied to simulate the flow around the spur-dike; the 270° curved open channel flow; the salt plume in the estuary to verify the applicability, efficient and stability. The results show that the model is efficient, stabile, reliable and can predict the three-dimensional characteristic of flow.