Simulation of rapidly varying flow using an efficient TVD-MacCormack scheme

International Journal for Numerical Methods in Fluids

Volumn 53, Issue 5, 2007, Pages 811-826

  Liang, Dongfang ^a   Lin, Binliang ^a   Falconer, Roger A ^a  

^a CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Conservation laws; Dam break; Numerical modelling; Shallow water flows; Shock capturing; Total variation diminishing

Indexed keywords

COMPUTER SIMULATION; DAMS; FINITE DIFFERENCE METHOD; FLOODS; MATHEMATICAL MODELS; SUPERCRITICAL FLUIDS;

CONSERVATION LAWS; COURANT NUMBER; DAM-BREAK; SHALLOW WATER EQUATIONS; SHOCK CAPTURING; TOTAL VARIATION DIMINISHING;

FLOW OF WATER;

COMPUTER SIMULATION; DAMS; FINITE DIFFERENCE METHOD; FLOODS; FLOW OF WATER; MATHEMATICAL MODELS; SUPERCRITICAL FLUIDS;

EID: 33846552938     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1305     Document Type: Article

References (25)

1. Leendertse JJ, Gritton EC. A water quality simulation model for well-mixed estuaries and coastal seas: vol. 2, computation procedures. Report No. R-708-NYC, The Rand Corporation, Santa Monica, 1971.
2. Falconer RA. Numerical modelling of tidal circulation in harbours. Journal of Waterway, Port, Coastal and Ocean Division (ASCE) 1980; 106:31-48.
3. Stelling GS, Wiersma AK, Willemse JBTM. Practical aspects of accurate tidal computations. Journal of Hydraulic Engineering (ASCE) 1986; 112:802-817.
4. Katopodes ND, Strelkoff T. Computing two-dimensional dam-break flood waves. Journal of Hydraulic Division (ASCE) 1978; 104:1269-1287.
5. Chen CL, Armbruster JT. Dam-break wave model: formulation and verification. Journal of Hydraulic Division (ASCE) 1980; 106:747-767.
6. Mools T, Chaudhry MH. Depth-averaged open-channel flow model. Journal of Hydraulic Engineering 1995; 121(6):453-465.
7. Mingham CG, Causon DM. High-resolution finite volume method for shallow water flows. Journal of Hydraulic Engineering 1998; 124(6):605-614.
8. Zoppou C, Roberts S. Catastrophic collapse of water supply reservoirs in urban areas. Journal of Hydraulic Engineering (ASCE) 1999; 125(7):686-695.
9. Rogers BD, Borthwick AGL, Taylor PH. Mathematical balancing of flux gradient and source terms prior to using Roe's approximate Riemann solver. Journal of Computational Physics 2003; 192:422-451.
10. Wang JS, Ni HG, He YS. Finite-difference TVD scheme for computation of dam-break problems. Journal of Hydraulic Engineering (ASCE) 2000; 126(4):253-262.
11. Tseng MH, Chu CR. Two-dimensional shallow water flows simulation using TVD-MacCormack scheme. Journal of Hydraulic Research 2000; 31:123-131.
12. Vincent S, Caltagirone J-P, Bonneton P. Numerical modelling of bore propagation and run-up on sloping beaches using a MacCormack TVD scheme. Journal of Hydraulic Research 2001; 39(1):41-49.
13. Lin GF, Lai JS, Guo WD. Finite-volume component-wise TVD scheme for 2D shallow water equations. Advances in Water Resources 2003; 26:861-873.
14. Rogers B, Fujihara M, Borthwick AGL. Adaptive Q-tree Godunov-type scheme for shallow water equations. International Journal for Numerical Methods in Fluids 2001; 35:247-280.
15. Liang D, Falconer RA, Lin B. Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations. Advances in Water Resources 2006, http://dx.doi.org/10.1016/j.advwatres.2006.01.005
16. Davis SF. TVD finite difference schemes and artificial viscosity. ICASE Report No. 84-20, NASA CR 172373, ICASE, NASA Langley Research Center, Hampton, 1984.
17. Louaked M, Hanich L. TVD scheme for the shallow water equations. Journal of Hydraulic Research 1998; 36:(3):363-378.
18. Mingharn CG, Causon DM, Ingram DM. A TVD MacCormack scheme for transcritical flow. Proceedings of the Institution of Civil Engineers, Water and Maritime Engineering 2001; 148(3):167-175.
19. Garcia-Navarro P, Vazquez-Cendon ME. On numerical treatment of the source terms in the shallow water equations. Computers and Fluids 2000; 29:951-979.
20. Tseng MH. The improved surface gradient method for flows simulation in variable bed topography channel using TVD-MacCormack scheme. International Journal for Numerical Methods in Fluids 2003; 43:71-91.
21. Liang D, Falconer RA, Lin B. Improved numerical modelling of estuarine flows. Proceedings of the Institution of Civil Engineers; Maritime Engineering 2006; 159(1):25-35.
22. Liang Q, Borthwick AGL, Stelling G. Simulation of dam- and dyke-break hydrodynamics on dynamically adaptive quadtree grids. International Journal for Numerical Methods in Fluids 2004; 46:127-162.
23. Fraccarollo L, Toro EF. Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems. Journal of Hydraulic Research 1995; 33:843-864.
24. Gottardi G, Venutelli M. Central scheme for two-dimensional dam-break flow simulation. Advances in Water Resources 2004; 27:259-268.
25. Testa G. (ed.). Third CADAM Meeting Proceedings. Milan: Italy, 1999.