Extension of ENO and WENO schemes to one-dimensional sediment transport equations

Computers and Fluids

Volumn 33, Issue 1, 2004, Pages 31-56

  Crnjaric Zic N ^a   Vukovic S ^a   Sopta, L ^a  

^a University of Rijeka   (Croatia)

Author keywords

Bed load sediment transport; Conservation law; ENO and WENO schemes; Exact conservation property; Nonconservative product

Indexed keywords

APPROXIMATION THEORY; LOAD TESTING; NUMERICAL METHODS; PROBLEM SOLVING; SOIL MECHANICS;

NONCONSERVATIVE PRODUCTS;

SEDIMENT TRANSPORT;

DEBRIS; MATHEMATICAL MODELING; ONE-DIMENSIONAL FLOW; SEDIMENT TRANSPORT;

EID: 0041841219     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7930(03)00032-X     Document Type: Article

References (18)

1. Bermùdez A. Dervieux A. Désidéri J.A. Vázquez M.E. Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes Comput. Meth. Appl. Mech. Eng. 155 1998 49
2. Bermùdez A. Vázquez M.E. Upwind methods for hyperbolic conservation laws with source terms Comput. Fluids 23 8 1994 1049
3. Harten A. Osher S. Uniformly high-order accurate non-oscillatory schemes I SIAM J. Numer. Anal. 24 1987 279
4. Harten A. Engquist B. Osher S. Chakravarthy S.R. Uniformly high order accurate essentially non-oscillatory schemes III J. Comput. Phys. 71 1987 231-303
5. Shu C.-W. Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes II J. Comput. Phys. 83 1989 32
6. Hubbard ME, Garcia-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients. Numerical Analysis Report, University of Reading, Department of Mathematics, 1999
7. Hudson J. Numerical techniques for morphodynamic modelling. Doctor Thesis, University of Reading, Department of Mathematics, 2001. A colour postscript version can be obtained at http://www.rdg.ac.uk/AcaDepts/sm/wsm1/research/theses/jh.html
8. Hudson J, Sweby PK. Numerical formulations for approximating the equations governing the bed-load sediment transport in channels and rivers. Numerical Analysis Report, University of Reading, Department of Mathematics, 2, 2000
9. LeVeque RJ. 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
10. van Rijn L.C. Sediment transport, Part I: bed-load transport Proc. ASCE J. Hydraul. Div. 110 HY 10 1984 1613
11. Liu X.-D. Osher S. Chan T. Weighted essentially non-oscillatory schemes J. Comput. Phys. 115 1994 200
12. Shu C.-W. Essentially non-oscillatory and weighted essentially non-oscillatory shock-capturing schemes for hyperbolic conservation laws Cockburn B. Johnson C. Shu C.-W. Tadmor E. Advanced Numerical Approximation of Nonlinear Hyperbolic Equations Lecture Notes in Mathematics vol. 1697 1998 Springer
13. Castro M. Maćas J. Parés C. A Q-scheme for class of systems of coupled conservation laws with source term. Application to a two-layer 1-d shallow water system Math. Modell. Numer. Anal. 35 2001 107
14. Vuković S. Sopta L. Essentially non-oscillatory and weighted essentially non-oscillatory scheme with the exact C-property for one-dimensional shallow water equations J. Comput. Phys. 179 2002 593
15. Grass AJ. Sediment transport by waves and currents. SERC London Cent Mar Technol, Report No: FL29, 1981
16. Brufau P. Garciá-Navarro P. Ghilardi P. Natale L. Savi F. 1d Mathematical modelling of debris flow J. Hydraul. Res. 38 2000 435
17. Gosse L. A well-balanced scheme using non-conservative products designed for hyperbolic systems for conservation laws with source terms Math. Mod. Meth. Appl. Sci. 11 2001 339-365
18. Jiang G. Shu C.-W. Efficient implementation of weighted ENO schemes J. Comput. Phys. 126 1996 202