Modelling coastal barrier breaching flows with well-balanced shock-capturing technique

Computers and Fluids

Volumn 39, Issue 10, 2010, Pages 2051-2068

  Kuiry, Soumendra Nath ^a   Ding, Yan ^a   Wang, Sam S Y ^a  

^a The University of Mississippi   (United States)

Author keywords

Coastal flow; Finite volume method; Process based Model; Radiation stress; Shallow water equations; Storm surge; Supercritical flow

Indexed keywords

COASTAL FLOW; PROCESS-BASED MODELS; RADIATION STRESS; SHALLOW WATER EQUATIONS; STORM SURGE; SUPERCRITICAL FLOW;

COMPUTER SIMULATION; FINITE VOLUME METHOD; FLOODS; FLOW OF WATER; FLUID DYNAMICS; HYDRODYNAMICS; NUMERICAL ANALYSIS; STORMS;

INLET FLOW;

EID: 77956342492     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2010.07.015     Document Type: Article

References (48)

1. Glaister P. Approximate Riemann solutions of the shallow water equations. J Hydraul Res 1998, 26:293-306.
2. Hubbard M.E., Dodd N. A 2D numerical model of wave run-up and overtopping. Coast Eng 2002, 47:1-26.
3. Namin M., Lin B., Falconer R.A. Modelling estuarine and coastal flows using an unstructured triangular finite volume algorithm. Adv Water Res 2004, 27:1179-1197.
4. Fennema R.J., Chaudhry M.H. Explicit methods for 2-D transient free-surface flows. J Hydraul Eng 1990, 116:1013-1034.
5. Alcrudo F., García-Navarro P. A high-resolution Godunov-type scheme in finite volumes for the 2D shallow water equations. Int J Numer Methods Fluids 1993, 16:489-505.
6. Zhao D.H., Shen H.W., Tabios G.Q., Lai J.S., Tan W.Y. A finite-volume two-dimensional unsteady flow model for river basins. J Hydraul Eng 1994, 120:863-883.
7. Mingham C.G., Causon D.M. High-resolution finite-volume method for shallow water flows. J Hydraul Eng 1998, 124:605-614.
8. Roe P.L. Approximate Riemann solvers, parameter vectors and difference schemes. J Comput Phys 1981, 43:357-372.
9. Roe P.L. A basis for upwind differencing of the two-dimensional unsteady Euler equations. Numer Methods Fluid Dyn 1986, II. [Oxford University Press].
10. Roe P.L., Pike J. Efficient construction and utilization of approximate Riemann solutions. Comp Methods Appl Sc Eng 1984, 6:499-518.
11. Bermúdez A., Vázquez-Cendón M.E. Upwind methods for hyperbolic conservation laws with source terms. Comput Fluids 1994, 23:1049-1071.
12. Vázquez-Cendón M.E. Improved treatment of source terms in upwind schemes for the shallow water equations. J Comput Phys 1999, 148:497-526.
13. LeVeque R.J. Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave propagation algorithm. J Comput Phys 1998, 146:346-365.
14. Burguete J., García-Navarro P. Efficient construction of high-resolution TVD conservative schemes for equations with source terms: application to shallow water flows. Int J Numer Methods Fluids 2001, 37:209-248.
15. Zhou J.G., Causon D.M., Mingham C.G., Ingram D.M. The surface gradient method for the treatment of source terms in the shallow-water equations. J Comput Phys 2001, 168:1-25.
16. Xing Y., Shu C.-W. High order finite difference WENO schemes with the exact conservation property for the shallow water equations. J Comput Phys 2005, 208:206-227.
17. Kuiry S.N., Pramanik K., Sen D. Finite volume model for shallow water equations with improved treatment of source terms. J Hydraul Eng 2008, 134:231-242.
18. Ding Y., Wang S.S.Y., Jia Y. Development and validation of a quasi-three-dimensional coastal area morphological model. J Water Port Coast Ocean Eng 2006, 132:462-476.
19. Lin L, Demirbilek Z, Mase H, Zheng J, Yamada F. CMS-wave: a nearshore spectral wave processes model for coastal inlets and navigation projects. Coastal and hydraulic engineering technical report ERDC/CHL TR-08-13, US Army Engineer Research and Development Center, Vicksburg, Mississippi, USA; 2008.
20. Longuet-Higgins M.S., Stewert R.W. The changes in amplitude of short gravity waves on steady non-uniform currents. J Fluid Mech 1961, 10:529-549.
21. Demirbilek ZL, Lin L, Zundel A. WABED model in the SMS: part 2. Graphical interface. Coastal and hydraulic engineering technical report CHL-98-26, US Army Engineer Research and Development Center, Vicksburg, Mississippi, USA; 2007.
22. Mase H.K., Oki K., Hedges T.S., Li H.J. Extended energy-balance-equation wave model for multidirectional random wave transformation. Ocean Eng 2005, 32:961-985.
23. Nishimura H. Computation of nearshore current. Nearshore dynamics and coastal processes 1988, 271-291. University of Tokyo Press, Tokyo (Japan). K. Harikawa (Ed.).
24. Militello A, Reed CW, Zundel AK, Kraus NC. Two-dimensional circulation model M2D: version 2.0, report 1, technical documentation and user's guide. Coastal inlets research program technical report ERDC-CHL-TR-04-02, US Army Engineer Research and Development Center, Vicksburg, Mississippi, USA; 2004.
25. Falconer RA. Modelling of planform influence on circulation in harbors. In: Proceedings the seventeen coastal engineering conference, ASCE. New York: ASCE Pres; 1980. p. 2726-44.
26. Larson M., Kraus N.C. Numerical model of longshore current for bar and trough beaches. J Waterway Port Coast Ocean Eng 1991, 117:326-347.
27. Alcrudo F., García-Navarro P., Saviron J. Flux difference splitting for 1D open channel flow equations. Int J Numer Methods Fluids 1992, 14:1009-1018.
28. Nujic M. Efficient implementation of non-oscillatory schemes for the computation of free surface flow. J Hydraul Res 1995, 33:101-111.
29. Anastasiou K., Chan C.T. Solution of the 2D shallow water equations using the finite volume met hod on unstructured triangular meshes. Int J Numer Methods Fluids 1997, 24:1225-1245.
30. Valiani A., Caleffi V., Zanni A. Case study: malpasset dam-break simulation using two-dimensional finite volume method. J Hydraul Eng 2002, 128:460-472.
31. Harten A., Hyman J.M. Self adjusting grid method for one-dimensional hyperbolic conservation laws. J Comput Phys 1983, 50:235-296.
32. Müller B. Numerische Lösung der kompressiblen Navier-Stokes-Gleichungen. Lecture notes, Institute of Fluid Dynamics, ETH Zürich, Zurich; 1991.
33. Godunov S.K. A difference method for the numerical computation of continuous solutions of hydrodynamic equations [JPRS by US Dept of Commerce, Tans.]. Mat Sbornik 1959, 47:271-306. [Original work published 1960].
34. Osher S. Convergence of generalized MUSCL schemes. SIAM J Numer Anal 1985, 22:947-961.
35. Hirsch C. Numerical computation of internal and external flows, vol. 1 1988, John Wiley & Sons, New York, USA.
36. Caleffi V., Valiani A., Zanni A. Finite volume method for simulating extreme flood events in natural channels. J Hydraul Res 2002, 41:167-177.
37. Valiani A., Begnudelli L. Divergence form of bed slope source term in shallow water equations. J Hydraul Eng 2006, 132:652-665.
38. Sweby P.K. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J Numer Anal 1984, 21:995-1011.
39. Reed C.W., Militello A. Wave-adjusted boundary condition for longshore current in finite-volume circulation models. Ocean Eng 2005, 32:2121-2134.
40. Brufau P., García-Navarro P., Vázquez-Cendón M.E. Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography. Int J Numer Methods Fluids 2004, 45:1047-1082.
41. Zundel AK. Surface-water modeling system reference manual - version 9.2. Provo, UT: Brigham Young University, Environmental Modeling Research Laboratory; 2006.
42. Ding Y, Wang SSY. Development of a numerical model for simulating tidal and wave-induced currents in coastal inlets. In: Proceeding of the 7th international conference on hydroscience and engineering (ICHE 2006), Philadelphia; 2006. ISBN: 0977447405. http://idea.library.drexel.edu/handle/1860/1371.
43. Ding Y, Wang SSY. Development of a numerical model for simulating morphodynamic processes driven by tides and waves at a coastal inlet. In: Malcolm Spaulding, editor. Estuarine and coastal modeling, proceeding of the 10th international conference on estuarine and coastal modeling. Newport, Rhode Island; 2008. p. 862-78.
44. Goutal N, Maurel F. Technical report HE-43/97/016/A, Electricité de France, Département Laboratoire National d'hydraulique, France; 1997.
45. Brufau P., Vázquez-Cendón M.E., García-Navarro P. A numerical model for the flooding and drying of irregular domains. Int J Numer Methods Fluids 2002, 39:247-275.
46. Toro E.F. Shock-capturing methods for free-surface shallow flows 2001, Wiley, England.
47. Henderson F.M. Open channel flow 1966, MacMillan Company, NY (USA).
48. Wang J.S., Ni H.G., He Y.S. Finite-difference TVD scheme for computation of dam-break problems. J Hydraul Eng 2000, 126:253-262.