Source term treatment of SWEs using surface gradient upwind method

Journal of Hydraulic Research

Volumn 50, Issue 2, 2012, Pages 145-153

  Pu, Jaan Hui ^a   Cheng, Nian Sheng ^b   Tan, Soon Keat ^c   Shao, Songdong ^d  

^a NAZARBAYEV UNIVERSITY   (Kazakhstan)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^d UNIVERSITY OF BRADFORD   (United Kingdom)

Author keywords

Finite volume model; Harten Lax van Leer contact solver; monotonic upwind scheme; source term; surface gradient upwind method; well balanced scheme

Indexed keywords

FINITE VOLUME MODEL; HARTEN-LAX-VAN LEER-CONTACT SOLVER; SOURCE TERMS; SURFACE GRADIENTS; UP-WIND SCHEME; WELL- BALANCED SCHEMES;

EQUATIONS OF MOTION; FLOW FIELDS; GRADIENT METHODS;

NUMERICAL METHODS;

EXPERIMENTAL STUDY; FINITE VOLUME METHOD; FLOW MODELING; NUMERICAL MODEL; SHALLOW-WATER EQUATION; TOPOGRAPHY;

EID: 84859722072     PISSN: 00221686     EISSN: None     Source Type: Journal    
DOI: 10.1080/00221686.2011.649838     Document Type: Article

References (33)

1. Aureli, F., Maranzoni, A., Mignosa, P., Ziveri, C. (2008). A weighted surface-depth gradient method for the numerical integration of the2Dshallow water equations with topography. Adv. Water Resour. 31(7), 962-974.
2. Bermudez, A., Vazquez-Cendon, M.E. (1994). Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23(7), 1049-1071.
3. Brufau, P. (2000). Simulación bidimensional de flujos hidrodinámicos transitorios en gemotrías irregulares [Twodimensional simulation of hydrodynamic transitions for irregular geometries]. PhD Dissertation. Universidad de Zaragoza, Spain [in Spanish].
4. Burguete, J., Garcia-Navarro, P., Murillo, J. (2008). Friction term discretization and limitation to preserve stability and conservation in the 1D shallow-water model: Application to unsteady irrigation and river flow. Int. J. Num. Meth. Fluids 58(4), 403-425.
5. Caleffi, V., Valiani, A., Zanni, A. (2003). Finite volume method for simulating extreme flood events in natural channels. J. Hydraulic Res. 41(2), 167-177. (Pubitemid 36845042)
6. Caleffi,V.,Valiani, A., Bernini, A. (2006). Fourth-order balanced source term treatment in central WENO schemes for shallow water equations. J. Comput. Phys. 218, 228-245. (Pubitemid 44364189)
7. Caleffi, V., Valiani, A., Bernini, A. (2007). High-order balanced CWENO scheme for movable bed shallow water equations. Adv. Water Resour. 30(4), 730-741.
8. Canestrelli, A., Dumbser, M., Siviglia, A., Toro, E.F. (2010). Well-balanced high-order centred schemes on unstructured meshes for shallow water equations with fixed and mobile bed. Adv. Water Resour. 33(3), 291-303.
9. Garcia-Navarro, P., Vazquez-Cendon, M.E. (2000). On numerical treatment of the source terms in the shallow water equations. Comput. Fluids 29(7), 951-979.
10. Goutal, N., Maurel, F., eds. (1997). Proc. 2nd Workshop Dam-Break Wave Simulation, 1-192. Laboratoire National d'Hydraulique, Groupe Hydraulique Fluviale, Electricité de France, Paris.
11. Greenberg, J.M., Leroux, A.Y. (1996). A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Num. Anal. 33(1), 1-16. (Pubitemid 126431700)
12. Hu, K., Mingham, C.G., Causon, D.M. (1998). A bore-capturing finite volume method for open-channel flows. Int. J. Num. Meth. Fluids 28(7), 1241-1261. (Pubitemid 29109859)
13. Hu, K., Mingham, C.G., Causon, D.M. (2006). A mesh patching method for finite volume modelling of shallow water flow. Int. J. Num. Meth. Fluids 50(11), 1381-1404.
14. Kim, D.H., Cho, Y.S., Kim, H.J. (2008). Well-balanced scheme between flux and source terms for computation of shallowwater equations over irregular bathymetry. J. Eng. Mech. 134(4), 277-290.
15. Kuiry, S.N., Ding, Y., Wang, S.S.Y. (2010). Modelling coastal barrier breaching flows with well-balanced shock-capturing technique. Comput. Fluids 39(9), 2051-2068.
16. Kuiry, S.N., Pramanik, K., Sen, D. (2008). Finite volume model for shallow water equations with improved treatment of source terms. J. Hydraulic Eng. 134(2), 231-242.
17. Kuiry, S.N., Sen, D. (2009). Closure of Finite volume model for shallow water equations with improved treatment of source terms. J. Hydraulic Eng. 135(10), 1017.
18. LeVeque, R.J. (1998). Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wavepropagation algorithm. J. Comput. Phys. 146, 346-365. (Pubitemid 128347128)
19. Liang, Q., Borthwick, A.G.L. (2009). Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography. Comput. Fluids 38(2), 221-234.
20. Liang, Q., Marche, F. (2009). Numerical resolution of wellbalanced shallow water equations with complex source terms. Adv. Water Resour. 32(6), 873-884.
21. Mingham, C.G., Causon, D.M. (2008). A simple high-resolution advection scheme. Int. J. Num. Meth. Fluids 56(5), 469-484. (Pubitemid 351222121)
22. Mingham, C.G., Causon, D.M. (2000). Calculation of unsteady bore diffraction using a high resolution finite volume method. J. Hydraulic Res. 38(1), 49-56. (Pubitemid 30582955)
23. Morris, M. (2000). CADAM-EU concerted action on dambreak modeling. Report No. SR 571. HR Wallingford UK.
24. Murillo, J., Garcia-Navarro, P., Burguete, J. (2009). Time step restrictions for well-balanced shallow water solutions in nonzero velocity steady states. Int. J. Num. Meth. Fluids 60(12), 1351-1377.
25. Murillo, J., Garcia-Navarro, P., Burguete, J., Brufau, P. (2007). The influence of source terms on stability, accuracy and conservation in two-dimensional shallow flow simulation using triangular finite volumes. Int. J. Num. Meth. Fluids 54(5), 543-590. (Pubitemid 46851115)
26. Toro, E.F. (2001). Shock-capturing methods for free-surface shallow flows. Wiley, Chichester.
27. Toro, E.F., Garcia-Navarro, P. (2007). Godunov-type methods for free-surface shallow flows: A review. J. Hydraulic Res. 45(6), 736-751.
28. Tseng, M.H. (2004). Improved treatment of source terms in TVD scheme for shallow water equations. Adv.Water Resour. 27(6), 617-629.
29. Valiani, A., Begnudelli, L. (2006). Divergence form for bed slope source term in shallow water equations. J. Hydraulic Eng. 132(7), 652-665.
30. Valiani, A., Begnudelli, L. (2008). Closure of Divergence form for bed slope source term in shallow water equations. J. Hydraulic Eng. 134(5), 680-682.
31. Xing, Y., Shu, C.W. (2005). High order finite difference WENO schemes with the exact conservation property for the shallow water equations. J. Comput. Phys. 208, 206-227. (Pubitemid 40714221)
32. Zhou, J.G., Causon, D.M., Mingham, C.G., Ingram, D.M. (2001). The surface gradient method for the treatment of source terms in the shallow water equations. J. Comput. Phys. 168, 1-25. (Pubitemid 33668235)
33. Zhou, J.G., Causon, D.M., Ingram, D.M., Mingham, C.G. (2002). Numerical solutions of the shallow water equations with discontinuous bed topography. Int. J. Num. Meth. Fluids 38(8), 769-788. (Pubitemid 34209698)