Study on Three-dimensional Shallow Water Model with Inner-Outer Separated Modes and Its Flux Formulations
In this paper,a 3-D shallow water model based on unstructured mesh finite volume method is established.By jointly solving the governing equations of the interior and exterior models,the vertical integral equation for water level is obtained using the exterior model.The water level is then used as an input to solve the three-dimensional shallow water motion control equations in the interior model,and the k-ε model is applied for turbulent closure.A triangular mesh is used in the horizontal direction to achieve better boundary fitting,while a σ coordinate system is adopted in the vertical direction to accommodate terrain and water surface fluctuations.In order to select a high-precision,computationally efficient,and easy-to-implement flux calculation scheme,a comparative study is conducted on four horizontal flux calculation schemes:HLLC,Osher,FVS,and Roe.The schemes are tested and validated for dam break,slant-bottom dam break,and wind-induced flow processes.The results show that the HLLC scheme is computationally efficient and suitable for dry-wet transition with relatively high accuracy.Finally,the HLLC scheme is used to simulate the flow in a navigation channel,further demonstrating the capability of the established shallow water model to simulate complex three-dimensional shallow water flows.
Three-dimensional shallow water equationFinite volume methodUnstructured meshFlux discretization format
万方数据
维普
