An Exner-based coupled model for two-dimensional transient flow over erodible bed

• Published in: Journal of computational physics Vol. 229; no. 23; pp. 8704 - 8732
• Main Authors: Murillo, J., García-Navarro, P.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.11.2010; Elsevier
• Subjects: 2D weak solutions; Bank equilibrium; Bedload sediment transport; Computational techniques; Exact sciences and technology; Exner equation; Finite volume method; Mathematical methods in physics; Physics; Roe method; Shallow water; Bank equilibrium; 2D weak solutions; Bedload sediment transport; Finite volume method; Exner equation; Shallow water; Roe method; Partial differential equations; Two dimensional flow; Finite volume methods; Calculation methods; Exact solution; Space-time; Dynamics; First order; Hydrodynamic model; Flow velocity; Mathematical models; Initial value problems; Calculation; Power law; Shallow-water equations; Interaction parameter
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.08.006

Transient flow over erodible bed is solved in this work assuming that the dynamics of the bed load problem is described by two mathematical models: the hydrodynamic model, assumed to be well formulated by means of the depth averaged shallow water equations, and the Exner equation. The Exner equation is written assuming that bed load transport is governed by a power law of the flow velocity and by a flow/sediment interaction parameter variable in time and space. The complete system is formed by four coupled partial differential equations and a genuinely Roe-type first order scheme has been used to solve it on triangular unstructured meshes. Exact solutions have been derived for the particular case of initial value Riemann problems with variable bed level and depending on particular forms of the solid discharge formula. The model, supplied with the corresponding solid transport formulae, is tested by comparing with the exact solutions. The model is validated against laboratory experimental data of different unsteady problems over erodible bed.