Numerical Simulation Of 3-D Shallow Water Flow On Irregular Triangular Grids

It is essential to use high accuracy numerical schemes to simulate discontinuities. In this paper, a three-dimensional shallow water flow and a material transport numerical model based on the finite volume method are established. In theory, the flow surface elevation is computed from the depth integeration of the mass conservation equation, i.e. the external model. Velocity distributions along vertical direction are computed from three-dimensional shallow water flow governing equations. k-εequations are used for the closure of the governing equation. In numerical method, in order to increase numerical stability, three-dimensional velocity field is obtained implicitly. In order to fit the irregular boundary better, we adopted the unstructured triangular mesh for the horizontal plane; in the vertical direction,σcoordinate system is adopted for simplification of bottom and surface boundary condition; Osher's scheme is used to compute the numerical flux across the boundary of the triangular elements in horizontal direction, thus the model has a good property of conservation for physical quantiy, up-windy property, monotonic-reserving, high resolution in capturing discontinuity, and consistency between boundary procedure and internal scheme. Transportation equation is solved by TVD scheme and high order numerical eddy term is added into the scheme to make sure the model has the property of high resolution in capturing discontinuities and good numerical stability.The model is applied to simulate the evolution process of a cone-shaped contaminant cloud moving in the rotating field. The advection fluxes are computed by upwind scheme, central scheme and TVD scheme respectively. Modeled results indicate that TVD scheme is the best one in both keeping the shape of concentration and lower spurious orscilation.The model is also used to simulate the movement of flow in a dead zone connected to a reach of open channel. Sequence of vortices due to shear instability in the mixing layer are well simulted in terms of their generation, transportation, vanishing, and water surface oscillation in the dead zone.The velocity profile is also compred with the measured ones and good agreement is achieved.The model is applied to an ideal river estuary to simulate the process of the circulation induced by the salt front intrusion. Salinity distribution along horizontal plane and vertical section are obtained and water surface and velocity field along...