Numerical Modelling of Bedload Sediment Transport Dynamics Using a Modified Flux-Wave Approach

Hossein Mahdizadeh

Wednesday 1 july 2015

11:15 - 11:30h at Mississippi (level 1)

Themes: (T) Sediment management and morphodynamics, (ST) Sediment transport mechanisms and modelling

Parallel session: 9A. Sediment - Transport

The interaction between the water flow and the sediment transport is a contemporary hydraulic engineering problem needed to be simulated for a wide range of hydrodynamic systems such as sea, rivers and estuaries. Prediction models should be able to accurately evaluate the morphological evolution of the bed along with the variation of the water surface. Morphodynamic models are typically governed by the shallow water equations (SWEs) which predict the hydrodynamics of flows and the Exner equation utilized for the sediment transport approximation. These equations form a nonlinear system of hyperbolic conservation laws can be generally solved based on the simultaneous or splitting approaches. For the splitting method the Exner equation is first solved and the resulting bed profile update is used as a source term for the SWEs. One of the drawbacks of the method is the use of different time steps for each equation which causes instabilities in particular when the rapid bathymetry deviations appeared in the solution. The simultaneous approach solves the entire set of the governing equations in a fully coupled form at each time step and thus it is inherently more stable. However, a main weakness of the method as reported in the literature is that, it has been only developed based on the non-conservative formulations and, no conservative solutions have yet been considered to the author’s knowledge. The main purpose of this paper is to device a fully conservative Godunov-type method for the bedload sediment transport modeling using the simulations solution. The proposed method will generalize a modified flux-wave approach (F-Wave) introduced by Mahdizadeh et al (2011) for the solution of the morphodynamic systems. This method is quite well-balanced and treats any source terms within the flux differencing of the finite-volume neighboring cells. Additionally, the approach can cope with the difficulties mentioned for the upwind solvers developed based on the non-conservative fluxes. To obtain basic understanding the problem is considered in 1D. It will be shown that the proposed method provides very good agreement with the analytical or reference solution even for the large Courant number relatively close to 1.