A Well-Balanced Scheme For Shallow Water Euqations Over Irregular Bed Topography Including Flooded And Partial Flooded Cells.

Fengpeng Bai, Zhonghua Yang

Tuesday 30 june 2015

9:45 - 10:00h at Europe 1 & 2 (level 0)

Themes: (T) Water engineering, (ST) Computational methods

Parallel session: 4E. Engineering - Computational

The depth-averaged shallow water equations are hyperbolic-type of conservation laws. Many numerical solutions have been developed to analyze the shallow water flows using the finite volume methods which have the advantage of properly handling with shock and contact discontinuities. However, there are some challenges in real applications due to the unbalance between the source and flux terms. The surface gradient method (SGM) is proposed by Zhou et al (2001), which is an attractive way to solve the shallow water equations with source terms. In this study, an improved surface gradient method (ISGM) is presented over irregular topography in a finite volume Godunov-type framework. Compared with the surface gradient method, in this method, the values of surface, velocity in the x and y direction are defined at the cell center; meanwhile, the values of water depth and topography are defined at the cell interface. The HLLC approximate Riemann solver is used to evaluate fluxes. The MUSCL reconstruction technique is applied for second-order spatial accuracy. In order to prevent numerical spurious oscillations near shocks, slope limiters are used. This model utilizes two-stage Runge-Kutta time integration method, and semi-implicit treatment for friction source terms. The numerical fluxes are corrected in the case of the water depth smaller than a fixed limiting value to keep the model stable in the presence of wetting and drying fronts. This method is validated by comparing the numerical results with the analytical solutions and laboratory experiments. Several test problems are conducted including tidal wave flows over an irregular bed, transcritical and subcritical flows, unsteady dam break flows on a wet and dry bed.