Abstract
Abstract In this work, a novel 2D depth-integrated numerical model for highly sediment-laden shallow flows over non-uniform erodible beds is presented, including variable density and exchange between the bed layer and the water–sediment mixture flow. The system of equations is formed by the 2D conservation equations for the mass and momentum of the mixture, the mass conservation equation for the different sediment size-classes transported in the flow and the bed evolution equation. The depth-averaged mixture density varies according to the volumetric concentration of the different sediment size-classes that can be incorporated from the bed to the flow and transported as suspended materials. The rheological behaviour of the flow is directly controlled by the properties of the mixture. A new x-split augmented Roe (xA-Roe) scheme is derived to solve the coupled flow and suspended solid-phase equations in both structured and unstructured meshes. The numerical scheme is defined to properly include density variations and momentum source terms, retaining a well-balanced flux formulation in steady states and the correct treatment of the wet–dry fronts. The numerical scheme is assessed with steady and transient cases involving highly sediment-laden flows, demonstrating its accuracy, stability and robustness in the presence of complex bed topography, wetting–drying fronts and rapid morphological changes.
Highlights
Water–sediment mixture flows are widely present in environmental and geophysical processes such as rivers and estuaries morphodynamics
The resulting system of equations is formed by the 2D conservation equations for the mass and momentum of the mixture, supplemented by the mass conservation equation for the different sediment size-classes suspended in the flow (Murillo et al ) and the bed variation equation
This paper is structured as follows: the two-dimensional quasi-single-phase equations for the water–sediment mixture with different suspended sizeclasses over non-uniform erodible bed are presented; The section “x-split augmented Roe (xA-Roe) Solver for 2D Sediment-Laden Flows” is devoted to describe the proposed xA-Roe scheme for variable-density flows, paying especial attention to the formulation of the numerical fluxes at the cell edges and the correct integration of the momentum source terms; in the section “Numerical results”, the numerical scheme is validated against steady-state cases with exact solution and idealized highly transient sediment-laden tests, demonstrating its stability and robustness in the presence of complex bed topography, wetting–drying fronts and rapid morphological changes; the conclusions are drawn in the final section
Summary
Water–sediment mixture flows are widely present in environmental and geophysical processes such as rivers and estuaries morphodynamics. This paper is structured as follows: the two-dimensional quasi-single-phase equations for the water–sediment mixture with different suspended sizeclasses over non-uniform erodible bed are presented; The section “xA-Roe Solver for 2D Sediment-Laden Flows” is devoted to describe the proposed xA-Roe scheme for variable-density flows, paying especial attention to the formulation of the numerical fluxes at the cell edges and the correct integration of the momentum source terms; in the section “Numerical results”, the numerical scheme is validated against steady-state cases with exact solution and idealized highly transient sediment-laden tests, demonstrating its stability and robustness in the presence of complex bed topography, wetting–drying fronts and rapid morphological changes; the conclusions are drawn in the final section. Where Ai is the cell area, (18) can be expressed as:
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