A novel well-balanced scheme for modelling of dam break flow in drying-wetting areas

Jia Mao, Lanhao Zhao

Thursday 2 july 2015

16:30 - 16:45h at Oceania (level 0)

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

Parallel session: 13E. Engineering - Computational

Dam break flows could lead to severe flooding with catastrophic consequences, such as damage to human lives and properties. In recent years, it has become compulsory to set up emergency plans for dam breaks. Numerical modeling and understanding of dam break flows are playing an increasingly essential role in hydraulic and river engineering in respect to reservoir safety. The finite element method (FEM) has been successfully employed in numerous applications due to its strict mathematical foundation and capability of handling complex geometries and boundary conditions exactly. However, two issues relevant in many applications are still under investigation: namely (i) preserving steady-states with variable ground elevation and (ii) properly handling drying and wetting. In this paper, a well-balanced explicit/semi-implicit finite element scheme is proposed for simulation of dam break flows over complex domains involving wetting and drying. The numerical model is based on the nonlinear shallow water equations in hyperbolic conservation form which can give a surprisingly accurate representation of dam-break flood due to its long wave hydrodynamics and the neglectable vertical acceleration of water particles. The governing equations are discretized by a fractional finite element method using a two-step Taylor-Galerkin scheme. Firstly, the intermediate increment of conserved variable is obtained explicitly neglecting the pressure gradient term. Then, the increment is corrected for the effects of pressure once the pressure increment has been obtained from the Poisson equation. In order to maintain the ‘well-balanced’ property, the pressure gradient term and bed slope terms are incorporated into the Poisson equation. Moreover, a local bed slope modification technique is employed in drying-wetting interface treatments. The new model is validated against several benchmark tests and laboratory experimental data related to dam-break flood wave propagation and promising results are obtained. Numerical results show that the model performs satisfactorily with respect to ability of resolving shocks, handling complex geometry, preserving well-balanced property and simulating the wetting and drying process.