Improvements of semi-implicit schemes for hyperbolic balance laws applied on open channel flow equations

Computers and Mathematics with Applications

Volumn 58, Issue 2, 2009, Pages 292-309

  Crnković, Bojan ^a   Črnjarić Žic, Nelida ^a   Kranjčević, Lado ^a  

^a University of Rijeka   (Croatia)

Author keywords

Hyperbolic balance law; Open channel equations; Semi implicit schemes; Upwind schemes and exact conservation property

Indexed keywords

BALANCE LAW; BED SLOPE; CFL NUMBER; CHANNEL GEOMETRY; CHANNEL WIDTHS; COMPUTATIONAL COSTS; CONSERVATION PROPERTIES; CROSS-SECTION GEOMETRY; FINITE VOLUME SCHEMES; HYPERBOLIC BALANCE LAW; KUPA RIVER; NONSTATIONARY; NONUNIFORM; NUMERICAL SCHEME; ONE PARAMETER FAMILY; OPEN CHANNEL EQUATIONS; PRE-COMPUTATION; REAL ENGINEERING; SAINT-VENANT; SEMI-IMPLICIT; SEMI-IMPLICIT APPROACH; SEMI-IMPLICIT SCHEME; SEMI-IMPLICIT SCHEMES; SIMULATION EFFICIENCY; TEST CASE; UNCONDITIONALLY STABLE; UPWIND SCHEMES AND EXACT CONSERVATION PROPERTY;

WALL FLOW;

OPEN CHANNEL FLOW;

EID: 67349282677     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.04.004     Document Type: Article

References (28)

1. Bermùdez A., and Vázquez M.E. Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23 (1994) 955-970
2. García-Navarro P., and Vázquez-Cendon M.E. On numerical treatment of the source terms in the shallow water equations. Comput. Fluids 29 (2000) 951-979
3. Hubbard M.E., and García-Navarro P. Flux difference splitting and the balancing of source terms and flux gradient. J. Comput. Phys. 165 (2000) 89-125
4. Burguette J., and Garcia-Navarro P. Efficient construction of high-resolution TVD conservative schemes for equations with source terms: Application to shallow water flows. Int. J. Numer. Methods Fluids 37 (2001) 209-248
5. Vuković S., and Sopta L. Upwind schemes with exact conservation property for one-dimensional open channel flow equations. SIAM J. Sci. Comput. 24 5 (2003) 1630-1649
6. Vuković S., Črnjarić-Žic N., and Sopta L. WENO schemes for balance laws with spatially varying flux. J. Comput. Phys. 199 (2004) 87-109
7. Črnjarić-Žic N., Vuković S., and Sopta L. Balanced finite volume WENO and central WENO schemes for the shallow water and the open channel flow equations. J. Comput. Phys. 200 (2004) 512-548
8. Xing Y., and Shu C.-W. High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. J. Comput. Phys. 214 (2006) 567-598
9. Chinnayya A., LeRoux A.Y., and Seguin N. A well-balanced numerical scheme for the approximation of the shallow-water equations with topography: The resonance phenomenon. Int. J. Finite Volumes 1 (2004)
10. A. Chinnayya, A.Y. LeRoux, A new general Riemann solver for the shallow water equations, with friction and topography. Available at: http://www.math.ntnu.no/conserva-tion/1999/021.html
11. Gosse L. A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms. Math. Models Methods Appl. Sci. 11 (2001) 339-365
12. Castro M., Gallardo J.M., and Parés C. High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow water systems. Math. Comput. 75 255 (2006) 1103-1134
13. Gallouet T., Hérard J.M., and Seguin N. Some approximate Godunov schemes to compute shallow water equations with topography. Comput. Fluids 32 (2003) 479-513
14. Bernetti R., Titarev V.A., and Toro E.F. Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry. J. Comput. Phys. 227 (2008) 3212-3243
15. Birman A., and Falkovitz J. Application of the GRP scheme to open channel flow equations. J. Comput. Phys. 222 (2007) 131-154
16. Audeusse E., Bouchut F., Bristeau M.O., Klein R., and Perthame B. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25 6 (2004) 2050-2065
17. Kurganov A., and Petrova G. A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system. Commun. Math. Sci. 5 (2007) 133-160
18. Harten A. On a class of high resolution total-variation-stable finite-difference schemes. SIAM J. Numer. Anal. 21 (1984) 1-23
19. Yee H.C. Construction of explicit and implicit symmetric TVD schemes and their applications. J. Comput. Phys. 68 (1987) 151-179
20. Yee H.C. Linearised form of implicit TVD schemes for the multidimensional Euler and Navier-Stokes equations. Comput. Math. Appl. 12 (1986) 413-432
21. Yee H.C., Warming R.F., and Harten A. Implicit total variation diminishing schemes (TVD) for steady state calculations. J. Comput. Phys. 57 (1985) 327-360
22. Alcrudo F., Garcia-Navarro P., and Priestley A. An implicit method for water flow modelling in channels and pipes. J. Hydraul. Res. 32 (1994) 721-742
23. Bermùdez A., Dervieux A., Desideri A., and Vázquez M.E. Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes. Comput. Methods Appl. Mech. Engrg. 155 (1998) 49-72
24. Delis A.I., Skeels C.P., and Ryrie S.C. Implicit high-resolution methods for modelling one-dimensional open channel flow. J. Hydraul. Res. 38 (2000) 369-382
25. Burguette J., and Garcia-Navarro P. Implicit schemes with large time step for non-linear equations: Application to river flow hydraulics. Int. J. Numer. Methods Fluids 46 (2004) 607-636
26. LeVeque R.J. Finite volume methods for hyperbolic problems. Cambridge Texts in Applied Mathematics (2002), Cambridge University Press, Cambridge, UK, New York
27. P. Goutal, F. Maurel, in: Proceedings of the 2nd Workshop on Dam-Break Wave Simulation, Technical Report HE-43/97/016A, Electicité de France, Département Laboratoire National d'Hydraulique, Groupe Hydraulique Fluviale, 1997
28. I. MacDonald, Analysis and computation of steady open channel flow, Ph.D. Thesis, University of Reading, Department of Mathematics, 1996