Abstract
The mathematical model describing the physical phenomenon of one-dimensional bed-load sediment transport in channels and rivers consists of three equations. Two of them represent conservation laws for one-dimensional shallow water equations, and third is the conservation law governing bed-load sediment transport. Here we considerone possibletype of the sediment flux proposed by Hudson and Sweby [7]. We compare numerical results for test problems using different numerical schemes: Q-scheme, Hubbard’s scheme, ENO Roe and ENO locally Lax-Friedrichs scheme. The obtained results illustrate good properties of ENO schemes with the source term decomposition, developed by authors. We also prove that these schemes have the exact C-property when applied to the sediment transport equations.
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References
A. Bermùdez, A. Dervieux, J. A. Désidén and M. E. Vazquez, Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes, Comput. Methods Appl. Mech. Eng. 155, 49 (1998).
A.Bermùdez and M. E. Vâzquez,Upwind methods for hyperbolic conservation laws with source terms, Comput.and Fluids 23 (8), 1049 (1994).
A.Harten and S.Osher, Uniformly high-order accurate non-oscillatory schemes 1,SIAM Journal on Numerical Analysis 24, 279 (1987).
A.Harten, B.Engquist, S.Osher and S.R.Chakravarthy, Uniformly high-order accurate non-oscillatory schemes III, Journal of Computational Physics 71, 231 (1987).
M. E.Hubbard and P. Garcia-Navarro, Flux difference splitting and the balancing of source terms and flux gradients, Numerical Analysis Report, University of Reading, Department of Mathematics, (1999).
J. Hudson, Numerical techniques for the shallow water equations, Numerical Analysis Report, University of Reading, Department of Mathematics, (1999).
J. Hudson and R. K. Sweby, Numerical Formulations for Approximating the Equations Governing Bed-Load Sediment Transport in Channels nad Rivers, Numerical Analysis Report, University of Reading, Department of Mathematics, (2000).
R. J. Leveque, Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave propagation algorithm, Numerical Analysis Report, Department of Applied Mathematics and Department of Mathematics, University of Washington, (1998).
L.C. van Rijn, Sediment Transport, Part I: Bed-Load Transport,Proc. ASCE Journal of Hydraulics Division, 110, HY 10, 1613 (1984)
C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory shock-capturing schemes for hyperbolic conservation laws, NASA/CR-97–206253, ICASE Report No. 97–65, Institute for Comp. App. in Science and Eng., NASA Langley Research Center, (1997).
J. Burguete and P. Garcia-Navarro, Efficient construction of high-resolution TVD conservative schemes for equations with the source terms: application to shallow water flows, Int. Journal for Numerical Methods in Fluids 37, 209 (2001)
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Sopta, L., Črnjarić-Žic, N., Vuković, S. (2002). Numerical Approximations of the Sediment Transport Equations. In: Drmač, Z., Hari, V., Sopta, L., Tutek, Z., Veselić, K. (eds) Applied Mathematics and Scientific Computing. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4532-0_16
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DOI: https://doi.org/10.1007/978-1-4757-4532-0_16
Publisher Name: Springer, Boston, MA
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