Two-dimensional depth-averaged finite volume model for unsteady turbulent flow

Abstract

A two-dimensional (2D) depth-averaged model is developed for simulating unsteady turbulent shallow-water flows with dry–wet fronts (e.g. dam-break flow). The model is based on 2D depth-averaged Reynolds-averaged Navier stokes equations coupled with the k−ϵ turbulence model. The high-resolution MUSCL scheme (monotone upstream-centred schemes for conservation laws) is implemented to minimize numerical diffusions. A novel augmented Harten–Lax–van Leer-contact Riemann solver is used to solve the governing equations simultaneously. A body-fitted mesh is generated by using the Cartesian cut-cell method to accommodate irregular boundaries. The model is tested against two laboratory experiments to examine whether or not turbulence model is essential for simulating unsteady turbulent flow. The results show that the addition of the k−ϵ turbulence model significantly improves the modelling results at places of strong turbulence activities. To further improve the results, a more accurate turbulence model for unsteady flow and dispersion terms in the momentum equations is needed.