A well-balanced explicit/semi-implicit finite element scheme for shallow water equations in drying-wetting areas

Abstract

Numerical solutions of the shallow water equations can be used to reproduce flow hydrodynamics occurring in a wide range of regions. In hydraulic engineering, the objectives include the prediction of dam break wave propagation, fluvial floods and other catastrophic flooding phenomena, the modeling of estuarine and coastal circulations, and the design and optimization of hydraulic structures. In this paper, a well-balanced explicit and semi-implicit finite element scheme for shallow water equations over complex domains involving wetting and drying is proposed. The governing equations are discretized by a fractional finite element method using a two-step Taylor–Galerkin scheme. First, the intermediate increment of conserved variable is obtained explicitly neglecting the pressure gradient term. This is then 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 proposed model is well validated against several theoretical benchmark tests.