A finite volume shock‐capturing solver of the fully coupled shallow water‐sediment equations. (7th February 2017)

• Record Type: Journal Article
• Authors: Creed, Maggie J.; Apostolidou, Ilektra‐Georgia; Taylor, Paul H.; Borthwick, Alistair G.L.
• Is Part Of: International journal for numerical methods in fluids. Volume 84:Number 9(2017)
• Page Start: 509
• Page End: 542
• Publication Date: 2017-02-07
• Subjects: shallow water‐sediment equations -- Riemann solver -- finite volume -- fully‐coupled -- suspended sediment -- bedload; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4359
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: This paper describes a numerical solver of well‐balanced, 2D depth‐averaged shallow water‐sediment equations. The equations permit variable horizontal fluid density and are designed to model water‐sediment flow over a mobile bed. A Godunov‐type, Harten–Lax–van Leer contact (HLLC) finite volume scheme is used to solve the fully coupled system of hyperbolic conservation laws that describe flow hydrodynamics, suspended sediment transport, bedload transport and bed morphological change. Dependent variables are specially selected to handle the presence of the variable density property in the mathematical formulation. The model is verified against analytical and semi‐analytical solutions for bedload transport and suspended sediment transport, respectively. The well‐balanced property of the equations is verified for a variable‐density dam break flow over discontinuous bathymetry. Simulations of an idealised dam‐break flow over an erodible bed are in excellent agreement with previously published results, validating the ability of the model to capture the complex interaction between rapidly varying flow and an erodible bed and validating the eigenstructure of the system of variable‐density governing equations. Flow hydrodynamics and final bed topography of a laboratory‐based 2D partial dam breach over a mobile bed are satisfactorily reproduced by the numerical model. Comparison of the final bed topographies, computed for two distinct sediment transport methods, highlights the sensitivity of shallow water‐sediment models to the choice of closure relationships. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : This paper describes an HLLC numerical Riemann solver of the fully coupled depth‐averaged shallow water‐sediment equations with variable mixture density and a mobile bed. Dependent variables are specially selected to preserve the variable density conservation property of the original mathematical formulation. The versatility of the model is demonstrated successfully by comparing numerical simulations against laboratory measurements of complicated dam break flows over erodible bed for both suspended sediment transport and bedload transport.