DAM BREAK FLOW ANALYSIS WITH APPROXIMATE RIEMANN SOLVER

  • Published : 2003.10.01

Abstract

A numerical model to analyze dam break flows has been developed based on approximate Riemann solver. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using finite volume method and the numerical flux are reconstructed with weighted averaged flux (WAF) method. The developed model is verified. The first verification problem is about idealized dam break flow on wet and dry beds. The second problem is about experimental data of dam break flow. From the results of the verifications, very good agreements have been observed

Keywords

References

  1. Bellos, C. V., Soulis, J. V., and Sakkas, J. G. (1992). 'Experimental investigation of two-dimensional dam-break induced flows.' Journal of Hydraulic Research, 30(1), 47-63
  2. Billett, S. J., Toro, E. F. (1997), 'On WAF-Type Schemes for Multidimensional Hyperbolic Conservation Laws,' Journal of Computational Physics, 130(1), 1-24 https://doi.org/10.1006/jcph.1996.5470
  3. Bradford, S. F., and Sanders, B. F. (2002), 'Finite-volume model for shallow-water flooding of arbitrary topography.' Journal of Hydraulic Engineering, ASCE, 128(3), 289-298 https://doi.org/10.1061/(ASCE)0733-9429(2002)128:3(289)
  4. Brocchini, M., Bernetti, R., Mancinelli, A., and Albertini, G. (2001), 'An efficient solver for nearshore flows based on the WAF method.' Coastal Engineering, 43, 105-129 https://doi.org/10.1016/S0378-3839(01)00009-6
  5. Glaister, P. (1988). 'Approximate Riemann solutions of the shallow water equations.' Journal of Hydraulic Research, 26(3), 293-306
  6. Hu, K., Migham, C.G., Causon, D. M. (2000). 'Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations.' Coastal Engineering, 41, 433-465 https://doi.org/10.1016/S0378-3839(00)00040-5
  7. Kim, D. H., Kim, W. G., Chae, H. S. and Park, S. G. (2002). 'Development of 2D Dam Break Flow Analysis Model using Fractional Step Method.' Water Engineering Research, 3(1), 23-30
  8. Mingham, C. G., and Causon, D. M. (1999). 'Calculation of unsteady bore diffraction using a high resolution finite volume method.' Journal of Hydraulic Research, 38(1), 49-56
  9. Fraccarollo, L., and Toro, E. F. (1995). 'Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems.' Journal of Hydraulic Research, 33(6), 843-864
  10. Fujihara, M., and Borthwick, G. L. (2000). 'Godunov-type solution of curvilinear shallow-water equation.' Journal of Hydraulic Engineering, ASCE, 126(11), 827-836 https://doi.org/10.1061/(ASCE)0733-9429(2000)126:11(827)
  11. Toro, E.F.(1999). Riemann solvers and numerical methods for fluid dynamics, Springer
  12. Toro, E.F.(2001). Shock-capturing methods for free-surface shallow flows. John Wiley & Sons, Ltd
  13. Wang, J.S., Ni, H.G., and He, Y.S. (2000). 'Finite-difference TVD scheme for Computation of dam-break problems.' Journal of Hydraulic Engineering, ASCE, 126(4), 253-262 https://doi.org/10.1061/(ASCE)0733-9429(2000)126:4(253)
  14. Zhao, D.H., Shen, H.W., Lai, J.S., and Tabios III, G.T.(1996). 'Approximate Riemann solvers in FVM for 2d hydraulic Engineering.' ASCE, 122(12), 692-702 https://doi.org/10.1061/(ASCE)0733-9429(1996)122:12(692)
  15. Zhao, D.H., Shen, H.W., Tabios III, G.Q., Lai, J.S., and Tan, W.Y. (1994). 'A finite volume two-dimensional unsteady flow model for river basins.' Journal of Hydraulic Engineering, ASCE, 120(7), 863-883 https://doi.org/10.1061/(ASCE)0733-9429(1994)120:7(863)
  16. Zoppou, C., and Stephen, R. (1999). 'Catastrophic collapse of water supply reservoirs in urban areas.' Journal of Hydraulic Engineering, ASCE, 125(7), 686-695 https://doi.org/10.1061/(ASCE)0733-9429(1999)125:7(686)
  17. Zoppou, C., and Stephen, R. (2000). 'Numerical solution of two-dimensional unsteady dam break.' Applied Mathematical Modelling, 24, 457-475 https://doi.org/10.1016/S0307-904X(99)00056-6