Preliminary Study On Coupled Surface And Subsurface Flow Model Based On FVM

In coastal waters, estuaries, lakes, rivers and the adjacent area, pollutant migration and diffusion, nutrient exchange, sediment transport, bed morphology, flood overflow etc. are closely related to the movement of surface water and groundwater. Developing numerical schemes and technique for surface and subsurface flows as well as numerical simulation of these flows is useful in understanding the laws and characteristic of the phenomena, and could provide a theoretical basis for engineering practice.On the basis of similarity of mathematical form of homogeneous shallow water equations (SWEs) and the Euler equations, finite volume method in modern shallow water simulation is originated from the high performance schemes in gas dynamics. However, homogeneous SWEs is only fit for flat terrain. For irregular terrain and problems with wetting and drying, special treatment is needed.Based on the balancing method proposed by other researchers, 1D and 2D finite volume models for surface flow over complex topography were developed, in which some approximate Riemann solvers such as Roe, HLL, Osher were used to calculate the numerical flux. High order schemes were obtained by MUSCL or upwind reconstruction, along with the use of limiters. The performance of different limiters was also examined. Besides, a simple and efficient method was proposed to deal with moving-boundary problems. A number of classic tests were employed to testify the model, including tidal wave flow over complex topography, a variety of dam-break problems, steady flow over a bump etc.Extended shallow water equations (ESWEs) for both surface water and groundwater were obtained based on the original SWEs. Then a coupled finite volume scheme was applied to the ESWEs, which was used to study the interaction of surface and subsurface flows. The coupled model was verified against the analytical solution for steady groundwater flow and the experimental data of tidal flow across an embankment. The results include that the surface flow model is able to simulate different flow regimes such as steady and unsteady, subcritical and supercritical flows, and break with second order accuracy and high resolution. The novel method for wetting and drying proposed in this paper is capable of tracing the moving shoreline, and global mass conservation property is well satisfied. The coupled model which simulates surface and subsurface flows simultaneously at the same time level can be used to study the water table fluctuations for both vertical and sloping beaches.