Advanced Numerical Solver for Dam-Break Flow Application
DOI:
https://doi.org/10.18321/ectj102Abstract
In this paper, a HLL (Harten Lax van Leer) approximate Riemann solver with MUSCL scheme (Monotonic Upwind Schemes for Conservative Laws) is implemented in the presented FV (Finite Volume) model. The presented model is used to simulate different dam-break flow events to verify its capability. Four test cases are presented in this paper. In the first test case, a 1-Dimensional (1D) dambreak flow is simulated over a rectangular channel with different slope limiters of the FV model (namely Godunov, Superbee, Minmod, van Leer, and van Albada). The second test case consists of a simulation of shallow water discontinuous dam-break flow over a dry-downstream bed channel. The third test simulates the shallow water dam-break flow with the existence of bed slope and bed shear stress. Finally, in the last test, the HLL-MUSCL model used in this paper and some other solver models used in literature are compared against the referred exact solution in dam-break flow application. The presented HLL-MUSCL scheme is found to give the best agreement to the exact solution.
References
2. M.H. Tseng, Explicit Finite Volume NonOscillatory Schemes for 2D Transient FreeSurface Flows, Int. J. Numer. Meth. Fluids, 30:831-843, 1999.
3. A.K. Jha, J. Akiyama, and M. Ura, High Resolution Flux-Difference-Splitting Scheme on Adaptive Grid for Open-Channel Flows, Int. J. Numer. Meth. Fluids, 36: 35-52, 2001.
4. M. Seaid, Non-Oscillatory Relaxation Methods for the Shallow-Water Equations in One and two Space Dimensions, Int. J. Numer. Meth. Fluids, 46: 457-484, 2004.
5. M. H. Tseng, and C. R. Chu, TwoDimensional Shallow Water Flows Simulation using TVD-MacCormack Scheme, J. Hydr. Res., 38(2): 123-131, 2000.
6. S. Vincent, J. P. Caltagirone, and P. Bonneton, Numerical Modelling of Bore Propagation and Run-up on Sloping Beaches using a MacCormack TVD Scheme, J. Hydr. Res., 39(1): 41-49, 2001.
7. G.F. Lin, J. S. Lai, and W. D. Guo, FiniteVolume Component-Wise TVD Schemes for 2D Shallow Water Equations, Adv. Wat. Resour., 26: 861-873, 2003.
8. P. Batten, M.A. Leschziner, and U. C. Goldberg, Average-State Jacobians and Implicit Methods for Compressible Viscous and Turbulent Flows, J. Comput. Phys., 137: 38-78, 1997.
9. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: a Practical Introduction, Springer-Verlag, Berlin, Germany, 1999.
10. K. Hu, C. G. Mingham, and D. M. Causon, A Bore-Capturing Finite Volume Method for Open-Channel Flows, Int. J. Numer. Meth. Fluids, 28: 1241-1261, 1998.
11. C. G. Mingham, and D. M. Causon, HighResolution Finite-Volume Method for Shallow Water Flows, J. Hydr. Engrg., 124(6): 605-614, 1998.
12. K. Hu, C. G. Mingham, D. M. Causon, A Mesh Patching Method for Finite Volume Modelling of Shallow Water Flow. Int. J. Num. Meth. Fluids, 50(12): 1381-1404, 2006.
13. A. I. Delis, C. P. Skeels, and S. C. Ryrie, Implicit High-Resolution Methods for Modelling One-Dimensional Open Channel Flow, J. Hydr. Res., 38(5): 369-382, 2000.
14. P.L. Roe, Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes, J. Comput. Phys., 43: 357-372, 1981.
15. N.P. C. Marques, and J. C. F. Pereira, Comparison of Three Second-Order Accurate Reconstruction Schemes for 2D Euler and Navier-Stokes Compressible Flows on Unstructured Grids, Commun. Numer. Meth. Eng., 17: 309-323, 2001.
16. S. K. Godunov, Finite Difference Method for Numerical Computation of Discontinuous Solutions of the Equations of Fluid Dynamics, Mat. Sb., 47(3): 271-306, 1959.
17. A. Harten, P. D. Lax, and B. van Leer, On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws, SIAM Rev., 25(1): 35-61, 1983.
18. A. Valiani, V. Caleffi, and A. Zanni, Case Study: Malpasset Dam-Break Simulation using a Two-Dimensional Finite Volume Method, J Hydr. Engrg., 128(5): 460-472, 2002.
19. V. Caleffi, A. Valiani, and A. Zanni, Finite Volume Method for Simulating Extreme Flood Events in Natural Channels, J Hydr. Res., 41(2): 167-177, 2003.
20. A. I. Delis, Improved Application of the HLLE Riemann Solver for the Shallow Water Equations with Source Terms, Commun. Numer. Meth. Engng., 19: 59-83, 2003.
21. A.A. Khan, Modeling Flow over an Initially Dry Bed, J. Hydr. Res., 38(5): 383-388, 2000.
22. J.H. Pu, N.-S. Cheng, S. K. Tan, and S. Shao, Source Term Treatment of SWEs using Surface Gradient Upwind Method, J. Hydr. Res., 2012, (In Press, doi:10.1080/00221686.2011.649838).
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