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Simulations of Dam-Break Flows Using Free Surface Capturing Method

Published online by Cambridge University Press:  05 May 2011

W.-Y. Chang ,
L.-C. Lee ,
H.-C. Lien  and
J.-S. Lai
W.-Y. Chang*
Affiliation:
National Center for High-Performance Computing, Hsinchu, Taiwan 10608, R.O.C
L.-C. Lee*
Affiliation:
National Center for High-Performance Computing, Hsinchu, Taiwan 10608, R.O.C
H.-C. Lien*
Affiliation:
National Center for High-Performance Computing, Hsinchu, Taiwan 10608, R.O.C
J.-S. Lai*
Affiliation:
Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
* Associate Researcher
* Associate Researcher
* Associate Researcher
** Associate Research Fellow, corresponding author
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Abstract

A model adopting the surface capturing method is developed for the simulation of dam-break flows by solving the Navier-Stokes equations of weakly compressible and variable density flows in open channels. Due to the characteristics of weakly compressible flow equations, a compressibility parameter describing the compressibility of fluid is determined to obtain the time-accurate flow fields in both liquid and gas regions simultaneously. Accordingly, the location of free surface can be captured as a discontinuity of the density field for dam-break flow simulations. The numerical algorithm in the proposed method is based on the framework of the finite volume method for discretization in space. To deal with the discontinuity property of fluid density near the free surface, the TVD-MUSCL scheme is adopted to overcome numerical oscillations and dissipation. For discretization in time, the explicit 4-stage Runge-Kutta scheme is employed in the model. Finally, several typical dam-break flow problems in open channel are simulated to demonstrate the validation and applicability of the proposed model.

Keywords

Weakly compressible flowsSurface capturing methodTVD-MUSCL schemeDam-Break flows
Type
Articles
Information
Journal of Mechanics , Volume 24 , Issue 4 , December 2008 , pp. 391 - 403
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2008

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References

1.Hirt, C. W., Nichols, B. D. and Romero, N. C., “SOLA — A Numerical Solution Algorithm for Transient Fluid Flows,” Los Alamos Scientific Laboratory Report: LA-5852, (1975).CrossRefGoogle Scholar
2.Hansbo, P., “Lagrangian Incompressible Flow Computations in Three Dimensions by Use of Space-Time Finite Elements,” Int. J. Numer. Meth. Fluids, 20, pp. 989–1001 (1995).CrossRefGoogle Scholar
3.LeVeque, R. J. and Shyue, K. M., “Two Dimensional Front Tracking Based on High Resolution Wave Propagation Methods,” J. Comput. Phys., 123, pp. 354–368 (1996).CrossRefGoogle Scholar
4.Harlow, F. H. and Welch, J. E., “Numerical Study of Large-Amplitude Free-Surface Motions,” Phys. Fluids, 9, pp. 842–851(1966).CrossRefGoogle Scholar
5.Hirt, C. W. and Nichols, B. D., “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Comput. Phys., 39, pp. 201–225 (1981).CrossRefGoogle Scholar
6.Hao, Y. and Prosperetti, A., “A Numerical Method for Three-Dimensional Gas-Liquid Flow Computations,” J. Comp. Phys., 196, pp. 126–144 (2004).CrossRefGoogle Scholar
7.Lohner, R., Yang, C. and Onate, E., “Simulation of Flows with Violent Free Surface Motion and Moving Objects Using Unstructured Grids,” Int. J. Numer. Meth. Fluids, 53, pp. 1315–1338 (2007).CrossRefGoogle Scholar
8.Medale, M., and Jaeger, M., “Numerical Simulations of Incompressible Flow with Moving Interfaces,” Int. J. Numer. Meth. Fluids, 24, pp. 615–638 (1997).3.0.CO;2-H>CrossRefGoogle Scholar
9.Kelecy, F. J., and Pletcher, R. H., “The Development of a Free Surface Capturing Approach for Multidimensional Free Surface Flows in Closed Containers,” J. Comput. Phys., 138, pp. 939–980 (1997).CrossRefGoogle Scholar
10.Lock, N., Jaeger, M., Medale, M. and Occelli, R., “Local Mesh Adaptation Technique for Front Tracking Problems,” Int. J. Numer. Meth. Fluids, 28, pp. 719–736(1998).3.0.CO;2-C>CrossRefGoogle Scholar
11.Maronnier, V., Picasso, M. and Rappaz, J., “Numerical Simulation of Free Surface,” J. Comput. Phys., 155, pp. 439–455 (1999).CrossRefGoogle Scholar
12.Coppola-Owen, A. H. and Codina, R., “Improving Eulerian Two-Phase Flow Finite Element Approximation with Discontinuous Gradient Pressure Shape Functions,” Int. J. Numer. Meth. Fluids 49, pp. 1287–1304 (2005).CrossRefGoogle Scholar
13.Ramaswamy, B., “Numerical Simulation of Unsteady Viscous Free Surface Flow,” J. Comput. Phys., 90, pp. 396–430 (1990).CrossRefGoogle Scholar
14.Lewis, R. W., Navti, S. E. and Taylor, C., “A Mixed Lagragian-Eulerian Approach to Modeling Fluid Flow During Mould Filling,” Int. J. Numer. Meth. Fluids, 25, pp. 931–952(1997).3.0.CO;2-1>CrossRefGoogle Scholar
15.Brackbill, J. U., Kothe, D. B. and Zemach, C., “A Continuum Method for Modeling Surface Tension,” J. Comp. Phys., 100, pp. 335–354 (1992).CrossRefGoogle Scholar
16.Sussman, M., Smereka, S. J. and Osher, S., “A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow,” J. Comp. Phys., 114, pp. 146–159(1994).CrossRefGoogle Scholar
17.Caiden, R., Fedkiw, C. and Anderson, C., “A Numerical Method for Two-Phase Flow Consisting of Separate Compressible and Incompressible Regions,” J. Comp. Phys., 166, pp. 1–27(2001).CrossRefGoogle Scholar
18.Fedkiw, R. and Osher, S., “Level Set Methods: An Overview and Some Recent Results,” J. Comp. Phys., 169, pp. 463–502(2001).Google Scholar
19.Sussman, M., “A Second Order Coupled Level Set and Volume-of-Fluid Method for Computing Growth and Collapse of Vapor Bubbles,” J. Comp. Phys., 187, pp. 110–136(2003).CrossRefGoogle Scholar
20.Pulliam, T. H., “Artificial Dissipation Models for Euler Equations,” AIAAJ., 24, pp. 1931–1940 (1986).CrossRefGoogle Scholar
21.Jorgenson, P. and Chima, R., “An Unconditionally Stable Runge-Kutta Method for Unsteady Flow,” AIAA paper 89–0205 (1989).CrossRefGoogle Scholar
22.Arnone, A., “Multigrid Time-Accurate Integration of Navier-Stokes Equations,” AIAA, pp. 93–3361 (1993).CrossRefGoogle Scholar
23.Lai, J. S., Lin, G. F. and Guo, W. D., “Simulation of Hydraulic Shock Waves by Hybrid Flux-Splitting Schemes in Finite Volume Method,” Journal of Mechanics, 21, pp. 85–101 (2005).CrossRefGoogle Scholar
24.Lai, J. S., Lin, G. F. and Guo, W. D., “An Upstream Flux-Splitting Finite-Volume Scheme for 2D Shallow Water Equations,” Int. J. Numer. Meth. Fluids, 48, pp. 1149–1174(2005).CrossRefGoogle Scholar
25.Titarev, V. A. and Toro, E. F., “MUSTA Schemes for Multi-Dimensional Hyperbolic Systems: Analysis and Improvements,” Int. J. Numer. Meth. Fluids, 49, pp. 117–147(2005).CrossRefGoogle Scholar
26.Guo, W. D., Lai, J. S. and Lin, G. F., “Hybrid Flux-Splitting Finite-Volume Scheme for the Shallow Water Flow Simulations with Source Terms,” Journal of Mechanics, 23, pp. 229–244 (2007).CrossRefGoogle Scholar
27.Zoppou, C. and Roberts, S., “Explicit Schemes for Dam-Break Simulations,” J. Hydr. Engrg., 129, pp. 11–34 (2003).CrossRefGoogle Scholar
28.Chorin, A. J., “A Numerical Method for Solving Incompressible Viscous Flow Problems,” J. Comput. Phys., 2, pp. 12–26 (1967).CrossRefGoogle Scholar
29.Rogers, S.E., Kwak, D. and Kiris, C., “Numerical Solution of the Incompressible Navier-Stokes Equations for Steady and Time-Dependent Problems,” AIAA paper 89–0463 (1989).CrossRefGoogle Scholar
30.Song, C. C. S. and Yuan, M., “A Weakly Compressible Flow Model and Rapid Convergence Method,” J. Fluid Engrg., 110, pp. 441–445 (1988).CrossRefGoogle Scholar
31.Song, C. C. S. and Yuan, M., “Simulation of Vortex- Shedding Flow about a Circular Cylinder at High Reynolds Nymbers,” J. Fluid Engrg., 112, pp. 155–163 (1990).CrossRefGoogle Scholar
32.Song, C. C. S. and Zhou, F., “Simulation of Free Surface Flow Over Spillway,” J. Hydr. Engrg., 125, pp. 959–967 (1999).CrossRefGoogle Scholar
33.Yen, C. L., Lai, J. S. and Chang, W. Y., “Modeling of 3D Flow and Scouring Around Circular Piers,” Proc. Of the National Science Council, Part A: Physical Science and Engineering, 25, pp. 17–26 (2001).Google Scholar
34.Weiss, J. M. and Smith, W. A., “Preconditioning Applied to Variable and Constant Density Flows,” AIAA Journal, 33, pp. 2050–2057 (1995).CrossRefGoogle Scholar
35.Turkle, E., “Preconditioning Techniques in Computational Fluid Dynamics,” Annu. Rev. FluidMech., 31, pp. 385–416 (1999).CrossRefGoogle Scholar
36.Hsu, U. K., Tai, C. H. and Tsai, C. H., “All Speed and High-Resolution Scheme Applied to Three-Dimensional Multi-Block Complex Flow Field System,” Chinese J. Mech. A, 20, pp. 13–25 (2004).Google Scholar
37.Liou, M. S., “A Sequel to AUSM, Part II: AUSM+-Up for All Speeds,” J. Comp. Phys., 214, pp. 137–170 (2006).CrossRefGoogle Scholar
38.Unverdi, S. O. and Tryggvason, G., “A Front Tracking Method for Viscous, Incompressible Multi-Fluid Flows,” J. Comp. Phys., 100, pp. 25–37 (1992).CrossRefGoogle Scholar
39.Kataoka, I., “Local Instant Formulation of Two-Phase Flow,” Int. J. Numer. Meth. Fluids, 12, pp. 745–758 (1986).Google Scholar
40.Smagorinsky, J., “General Circulation Experiments with Primitive Equation,” Monthly Weather Review, 91, pp. 99–154 (1963).2.3.CO;2>CrossRefGoogle Scholar
41.Tannehill, J. C., Anderson, D. A. and Pletecher, R. H., Computational Fluid Mechanics and Heat Transfer, Taylor and Francis, Philadelphia (1997).Google Scholar
42.Toro, E. F., Shock-Capturing Methods for Free-Surface Shallow Water Flows, John Wiley and Sons, New York (2001).Google Scholar
43.Ferziger, J. H. and Peric, M., Computational Methods for Fluid Dynamics, Springer, New York (1999).CrossRefGoogle Scholar
44.Roe, P. I., “Characteristic-Based Schemes for Euler Equations,” Annu. Rev. Fluid Mech., 18, pp. 337–365 (1986).CrossRefGoogle Scholar
45.Leonard, B. P., “A Stable and Accurate Convective Modeling Procedures Based on Quadratic Upstream Interpolation,” Comput. Methods Appl. Math., 19, pp. 59–98 (1979).Google Scholar
46.Schumann, U., “Subgrid Scale Models for Finite Difference Simulations of Turbulent Flows in Plane Channel and Annuli,” J. Comp. Phys., 18, pp. 376–404 (1975).CrossRefGoogle Scholar
47.LeVeque, R. J., Finite Volume Methods for Hyperbolic Problems Cambridge University Press, UK (2002).CrossRefGoogle Scholar
48.Aureli, F., Mignosa, P. and Tomirotti, M., “Numerical Simulation and Experimental Verification of Dam-Break Flows with Shocks,” J. Hydraul. Res., 38, pp. 197–206(2000).CrossRefGoogle Scholar
49.Fraccarollo, L. and Toro, E. F., “Experimental and Numerical Assessment of Shallow Water Model for 2D Dam-Break Type Problems,” J. Hydraul. Res., 33, pp. 843–864 (1995).CrossRefGoogle Scholar
50.Lin, G. F., Lai, J. S. and Guo, W. D., “High-Resolution TVD Schemes in Finite Volume Method for Hydraulic Shock Wave Modeling,” J. Hydraul. Res., 43, pp. 376–389 (2005).CrossRefGoogle Scholar