Godunov-type solution of the shallow water equations on adaptive unstructured triangular grids

International Journal of Computational Fluid Dynamics

Volumn 20, Issue 9, 2006, Pages 621-636

  Skoula, Z D ^a   Borthwick, A G L ^b   Moutzouris, C I ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Adaptive finite volume; Godunov; Implicit time integration; Shallow water equations; Unstructured grids; Variable bed topography

Indexed keywords

EID: 34547783242     PISSN: 10618562     EISSN: 10290257     Source Type: Journal    
DOI: 10.1080/10618560601088327     Document Type: Article

References (30)

1. Alcrudo, F. and García-Navarro, P., A high-resolution Godunov-type scheme in finite volumes for the 2D shallow water equations. Int. J. Numer. Meth. Fluids, 1993, 16, 489-505.
2. Anastasiou, K. and Chan, C.T., Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes. Int. J. Numer. Meth. Fluids, 1997, 24(11), 1225-1245.
3. Bank, R.E., The efficient implementation of local mesh refinement algorithms. Adaptive Computational Methods for Partial Differential Equations, 1983 (SIAM: Philadelphia).
4. Borthwick, A.G.L. and Barber, R.W., Prediction of low Reynolds number jet-forced flow inside a circle using the Navier-Stokes equations. Int. J. Eng. Fluid Mech., 1990, 3(4), 323-343.
5. Chippada, S., Dawson, C.N., Martinet, M.L. and Wheeler, M.F., A Godunov-type finite volume method for the system of shallow water equations. Comput. Meth. Appl. Mech. Eng., 1998, 151, 105-129.
6. Dennis, S.C.R., Application of the series truncation method to two-dimensional internal flows. Proceedings of the 4th International Conference on Numerical Methods In Fluids Dynamics, pp. 146-151, 1974 (University of Colorado, Springer).
7. Fraccarollo, L. and Toro, E.F., Experimental and numerical assessment of the shallow water model for two-dimension dam-break, type problems. J. Hydr. Res., 1.995, 33(6), 843-863.
8. George, P.L., Automatic Mesh Generation: Application to Finite Element Methods, 1991 (Wiley & Sons: New York).
9. Hager, W.H., Schwalt, M., Jimenez, O. and Chaudhry, M.H., Supercritical flow near an abrupt wall deflection. J. Hydr. Res., 1994, 32(1), 103-118.
10. Hirsch, C., Numerical Computation of Internal and External Flows, Vol. 2: Computational Methods for Inviscid and Viscous Flows, 1990 (John Wiley & Sons: New York).
11. Hubbard, M. and Dodd, N., A 2D numerical model of wave run-up and overtopping. Coastal Eng., 2002, 47, 1-26.
12. Hubbard, M. and García-Navarro, P., Flux difference splitting and the balancing of source terms and flux gradients. J. Comput. Phys., 2000, 165, 89-125.
13. Kranenburg, C., Wind driven chaotic advection in a shallow model, lake. J. Hydr. Res., 1992, 30(1), 29-46.
14. LeVeque, R.J., Finite Volume Methods: for Hyperbolic Problems, 2002 (Cambridge University Press: New York).
15. Mingham, C.G. and Causon, D.M., A high resolution finite volume method for the shallow water equations. J. Hydr. Eng., 1998, 124(6), 605-614.
16. Nugic, M., Efficient implementation of non-oscillatory schemes for the computation of free surface flows. J. Hydr. Res., 1995, 33(1), 101-111.
17. Pan, D. and Cheng, J.C., A second-order upwind finite-volume method for the Euler solution on unstructured triangular meshes. Int. J. Numer. Meth. Fluids, 1993, 16, 1079-1098.
18. Pan, D. and Lomax, H., A new approximate LU factorisation scheme for the Reynolds-averaged Navier-Stokes equations. AIAA J., 1988, 26(2), 163-171.
19. Rogers, B., Borthwick, A.G.L. and Taylor, P.H., Balancing flux gradients and source terms with Roe's approximate Riemann solver. J. Comput. Phys., 2003, 192(2), 422-451.
20. Skoula, Z.D., Refined Localised Modelling of Coastal Flow Features Using Unstructured Grids, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, 2002 (University of London: U.K.).
21. Sleigh, P.A., Gaskell, P.H., Berzins, M. and Wright, N.G., Unstructured finite-volume algorithm for predicting flow in rivers and estuaries. Comput. Fluids, 1998, 27(4), 479-508.
22. Soulsby, R., Dynamics of Marine Sands: a Manual for Practical Applications, 1998 (Thomas Telford: London).
23. Strouboulis, T. and Haque, K.A., Recent experiences with error estimation and adaptivity. Part I: review of error estimators for scalar elliptic problems. Comput. Meth. Appl. Mech. Eng., 1992, 97, 399-436.
24. Thompson, J.F., Soni, B.K. and Weatherill, N.P., Handbook of Grid Generation, 1999 (CRC Press LLC: Boca Raton).
25. Toro, E.F., Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, 1997 (Springer-Verlag: Berlin).
26. Toro, E.F., Shock-Capturing Methods for Free-Surface Shallow Flows, 2001 (John Wiley: Chichester).
27. Vázquez-Cendón, M.E., Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comput. Phys., 1999, 148, 497-526.
28. Zhao, D.H., Shen, H.W., Tabious, III G.Q., Lai, S.J. and Tan, W.Y., Finite-volume two-dimensional unsteady-flow model for river basins. J. Hydr. Eng. ASCE, 1994, 120(7), 864-883.
29. Zhou, J.G., Causon, D.M., Ingram, D.M. and Mingham, C.G., Numerical solutions of the shallow water equations with discontinuous bed topography. Int. J. Numer. Meth. Fluids, 2002, 38, 769-788.
30. Zoppou, C. and Roberts, S., Numerical solution of the two-dimensional unsteady dam break. Appl. Math. Modelling, 2000, 24, 457-475.