Combined finite volume-finite element method for shallow water equations

Computers and Fluids

Volumn 34, Issue 10, 2005, Pages 1199-1222

  Wang, Ji Wen ^a,b   Liu, Ru Xun ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b ANHUI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; GALERKIN METHODS; MATRIX ALGEBRA; NUMERICAL METHODS; RUNGE KUTTA METHODS; VECTORS; VISCOUS FLOW;

FINITE VOLUME-FINITE ELEMENT METHOD; SHALLOW WATER EQUATIONS;

FLOW OF WATER;

FINITE VOLUME TECHNIQUE;

EID: 23944476816     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2004.09.008     Document Type: Article

References (27)

1. V. Aizinger C. Dawson A discontinuous Galerkin method for two-dimensional flow and transport in shallow water Adv Water Resour 25 2002 67-84
2. F. Alcrudo P. Garcia-Navarro A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations Int J Numer Methods Fluids 16 1993 489-505
3. K. Anastasiou C.T. Chan Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes Int J Numer Methods Fluids 24 1997 1225-1245
4. F. Angrand A. Dervieux Some explicit triangular finite element schemes for Euler equations Int J Numer Methods Fluids 4 1984 749-764
5. Barth JT, Jespersen DC. The design and application of upwind schemes on unstructured meshes. AIAA Paper 89-0366, 1989.
6. A.G.L. Borthwick R.W. Barber River and reservoir modeling using the transformed shallow water equations Int J Numer Methods Fluids 14 1992 1193-1217
7. S.F. Bradford B.F. Sanders Finite-volume model for shallow-water flooding of arbitrary topography J Hydraul Eng 128 2002 289-298
8. M.K. Denham M.A. Patrick Laminar flow over a downstream-facing step in a two-dimensional flow channel Trans Inst Chem Eng 52 1974 361-367
9. K.S. Erduran V. Kutija C.J.M. Hewett Performance of finite volume solutions to the shallow water equations with shock-capturing schemes Int J Numer Methods Fluids 40 2002 1237-1273
10. M. Feistauer J. Felcman M. Lukacova-Medvidova Combined finite element-finite volume solution of compressible flow J Comput Appl Math 63 1995 179-199
11. S.K. Godunov A difference method for the numerical calculation of discontinuous solutions of hydrodynamic equations Mat Sbornik 47 1959 271-306 [in Russian]
12. L. Hallo C.L. Ribault M. Buffat An implicit mixed finite-volume-finite-element method for solving 3D turbulent compressible flows Int J Numer Methods Fluids 25 1997 1241-1261
13. K. Hu C.G. Mingham D.M. Causon A bore-capturing finite volume method for open-channel flows Int J Numer Methods Fluids 28 1998 1241-1261
14. M.E. Hubbard Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids J Comput Phys 155 1999 54-74
15. A. Karageorghis T. Tang A spectral domain decomposition approach for steady Navier-Stokes problems in circular geometries Comput. Fluids 25 1996 541-549
16. R. Liska B. Wendroff Two-dimensional shallow water equations by composite schemes Int J Numer Methods Fluids 30 1999 461-479
17. http://www-dinma.univ.trieste.it/nirftc/research/easymesh/easymesh.html
18. J. Pudykiewicz A. Staniforth Some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation Atmos-Ocean 22 1984 283-308
19. P.L. Roe Approximate Riemann solvers, parameter vectors and difference schemes J Comput Phys 43 1981 357-372
20. B. Rogers M. Fujihara A.G.L. Borthwick Adaptive Q-tree Godunov-type scheme for shallow water equations Int J Numer Methods Fluids 35 2001 247-280
21. C.W. Shu S. Osher Efficient implementation of essentially non-oscillatory shock capturing schemes J Comput Phys 77 1988 439-471
22. C.W. Shu TVB uniformly high order schemes for conservation laws Math Comput 49 1987 105-121
23. H.Z. Tang T. Tang K. Xu A gas-kinetic scheme for shallow-water equations with source terms Z Angew Math Phys 55 2004 365-382
24. J.W. Wang R.X. Liu A comparative study of finite volume methods on unstructured meshes for simulation of 2D shallow water wave problems Math Comput Simul 53 2000 171-184
25. J.W. Wang R.X. Liu The composite finite volume method on unstructured triangular meshes for 2D shallow water equations Int J Numer Methods Fluids 37 2001 933-949
26. D.H. Zhao H.W. Shen J.S. Lai G.Q. Tabios III Approximate Riemann solvers in FVM for 2D hydraulic shock wave problems J Hydraul Eng 122 1996 692-702
27. O.C. Zienkiewicz P. Ortiz A split-characteristic based finite element model for the shallow water equations Int J Numer Methods Fluids 20 1995 1061-1080