Abstract
This paper investigates the accurate numerical solution of the equations governing bed-load sediment transport. Two approaches: a steady and an unsteady approach are discussed and five different formulations within these frameworks are derived. A flux-limited version of Roe's scheme is used with the different formulations on a channel test problem and the results compared.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bermudez, A., and Vazquez, M. E. (1994). Upwind methods for hyperbolic conservation laws with source terms. Computers and Fluids 23, 1049-1071.
Burguete, J., and Garcia-Navarro, P. (2001). Efficient construction of high-resolution tvd conservative schemes for equations with source terms. Application to shallow water flows. Int. J. Numer Meth Fluids 37, 209-248.
Cunge, J. A., Holly, F. M., and Verway, A. (1980). Practical Aspects of Computational River Hydraulics, Pitman.
Damgaard, J. S. (1998). Numerical Schemes for Morphodynamic Simulations, HR Wallingford, Report IT 459.
De Vries, M. (1973). River-bed Variations—Aggradation and Degradation, I.H.A.R. International Seminar on Hydraulics of Alluvial Streams, New Dehli.
Embid, P., Goodman, J., and Majda, A. (1984). Multiple steady states for 1D transonic flow. SIAM J. Sci. Stat. Comput. 8, 21-41.
Glaister, P. (1987). Difference Schemes for the Shallow Water Equations, Numerical Analysis Report 9/97, University of Reading.
Grass, A. J. (1981). Sediment Transport by Waves and Currents, SERC London Cent. Mar. Technol, Report No: FL29.
Harten, A. (1983). High resolution schemes for conservation laws. J. Comput. Phys. 49.
Hubbard, M. E., and Garcia-Navarro, P. (2000). Flux difference splitting and the balancing of source terms and flux gradients. J. Comput. Phys. 165, 89-125.
Hudson, J. (2001). Numerical Techniques for Morphodynamic Modelling, Ph.D. thesis, University of Reading. A colour postscript version of this thesis can be obtained at www.rdg.ac.uk/maths.
Hudson, J., and Sweby, P. K. (2000). Numerical Formulations for Approximating the Equations Governing Bed-Load Sediment Transport in Channels and Rivers, Numerical Analysis Report 2/2000, University of Reading. A colour postscript version of this report can be obtained at www.rdg.ac.uk/maths.
Le Veque, R. J., and Yee, H. C. (1990). A study of numerical methods for hyperbolic conservation laws with stiff source terms. J. Comput. Phys. 86, 187-210.
Le Veque, R. J. (1998). Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm. J. Comput. Phys. 146, 346-365.
Roe, P. L. (1981). Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys. 43, 357-372.
Roe, P. L. (1986). Upwind differencing schemes for hyperbolic conservation laws with source terms. In Carasso, C., Raviart, P. A., and Serre, D. (eds.), Proc. Nonlinear Hyperbolic Problems, Springer Lecture Notes in Mathematics, Vol. 1270, pp. 41-51.
Soulsby, R. L. (1997). Dynamics of Marine Sands, A Manual for Practical Applications, HR Wallingford, Report SR 466.
Spiegel, M. R., and Liu, J. (1999). Mathematical handbook of formulas and tables, 2nd edn., Schaum's Outline Series, McGraw–Hill, ISBN 0-07-038203-4.
Sweby, P. K. (1984). High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Num. Anal. 21, 995.
Zanré, D. D. L., and Needham, D. J. (1994). On the hyberbolic nature of the equations of alluvial river hydraulics and the equivalence of stable and energy dissipating shocks. Geophys. Astrophys. Fluid Dynamics 76, 193-222.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hudson, J., Sweby, P.K. Formulations for Numerically Approximating Hyperbolic Systems Governing Sediment Transport. Journal of Scientific Computing 19, 225–252 (2003). https://doi.org/10.1023/A:1025304008907
Issue Date:
DOI: https://doi.org/10.1023/A:1025304008907