A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

Abstract

Overland flow and soil erosion play an essential role in water quality and soil degradation.Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.

Keeping the edge: A numerical method that avoids knickpoint smearing when solving the stream power law

“…FVMs are frequently used in fluid dynamics. The method is not only extensively applied to simulate dam break problems [Zhao et al, 1994;Simpson and Castelltort, 2006] and tidal wave propagation [Hu et al, 1998] but also in river geomorphology, for example, to model water flow in meandering channels [Ye and McCorquodale, 1997] or more recently, to compute soil erosion and coupled sediment transport [Le et al, 2015]. In contrast to FDMs, FVMs consider the discrete values in a grid to represent the averages over finite volumes surrounding the nodes of this grid [Toro, 2009].…”

Constraining the relative importance of raindrop‐ and flow‐driven sediment transport mechanisms in postwildfire environments and implications for recovery time scales

“…We choose a Godunov-type method because of its shock-capturing properties, which allow it to deal naturally with dry/wet interfaces that may exist in the solution when overland flow is shallow and potentially discontinuous. Equations (28) and (29) are solved using explicit, first-order-in-time methods, but special care must be taken to prevent the computation of negative values for c k and m k where predicted erosion or deposition rates may be limited by the availability of sediment [e.g., Struiksma, 1999;Le et al, 2015]. Details of the numerical methods and several test cases, also found in Sander et al [1996Sander et al [ , 2002, are presented in the supporting information (Texts S1-S3).…”

Statistical Distribution of TSS Event Loads from Small Urban Environments

“…Being mainly adapted from soil erosion research, the model detaches particles proportional to rainfall intensity and masses available at surface. Reference [20] modelled the wash-off process of a small road near Paris using a model system coupling the shallow water equations for overland flow and the Hairsine-Rose model for sediment detachment and transport [21,22]. Results for water quantity and quality indicated a well agreement with in-situ observations.…”