Integrated numerical model for vegetated surface and saturated subsurface flow interaction

doi:10.1007/s10483-012-1592-9

摘要/Abstract

摘要： The construction of an integrated numerical model is presented in this paper to deal with the interactions between vegetated surface and saturated subsurface flows. A numerical model is built by integrating the previously developed quasi-three-dimensional (Q3D) vegetated surface flow model with a two-dimensional (2D) saturated groundwater flow model. The vegetated surface flow model is constructed by coupling the explicit finite volume solution of 2D shallow water equations (SWEs) with the implicit finite difference solution of Navier-Stokes equations (NSEs) for vertical velocity distribution. The subsurface model is based on the explicit finite volume solution of 2D saturated groundwater flow equations (SGFEs). The ground and vegetated surface water interaction is achieved by introducing source-sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The integrated model is applied to four test cases, and the results are satisfactory.

关键词: first-order differential equation, periodic solution, resonance, Brouwer degree, coincidence degree, Duffing equation, vegetated surface flow, saturated groundwater flow, flow interaction, tight coupling, finite volume method, finite difference method, flow resistance

Abstract: The construction of an integrated numerical model is presented in this paper to deal with the interactions between vegetated surface and saturated subsurface flows. A numerical model is built by integrating the previously developed quasi-three-dimensional (Q3D) vegetated surface flow model with a two-dimensional (2D) saturated groundwater flow model. The vegetated surface flow model is constructed by coupling the explicit finite volume solution of 2D shallow water equations (SWEs) with the implicit finite difference solution of Navier-Stokes equations (NSEs) for vertical velocity distribution. The subsurface model is based on the explicit finite volume solution of 2D saturated groundwater flow equations (SGFEs). The ground and vegetated surface water interaction is achieved by introducing source-sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The integrated model is applied to four test cases, and the results are satisfactory.

Key words: first-order differential equation, periodic solution, resonance, Brouwer degree, coincidence degree, Duffing equation, vegetated surface flow, saturated groundwater flow, flow interaction, tight coupling, finite volume method, finite difference method, flow resistance

中图分类号:

TV133

K. S. ERDURAN. Integrated numerical model for vegetated surface and saturated subsurface flow interaction[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(7): 881-898.

参考文献

[1] Tsujimoto, T. and Kitamura, T. Velocity Profile of Flow in Vegetated-Bed Channels, KanazawaUniversity, Khl Progressive Report 1, Kanazawa (1990)
[2] Fischenich, C. Resistance Due to Vegetation, EMRRP technical notes, ERDC TN-EMRRP-SR-07,US Army Engineer Research and Development Center, Vicksburg (2000)
[3] Erduran, K. S. and Kutija, V. Quasi three-dimensional numerical model for flow through flexible,rigid, submerged and non-submerged vegetation. Journal of Hydroinformatics, 5(3), 189-202(2003)
[4] Wu, F. C., Shen, H. W., and Chou, Y. J. Variation of roughness coefficients for unsubmerged andsubmerged vegetation. Journal of Hydraulic Engineering, 125(9), 934-942 (1999)
[5] Palmer, V. J. A method for designing vegetated waterways. Agricultural Engineering, 20(4), 516-520 (1945)
[6] Carollo, F. G., Ferro, V., and Termini, D. Flow velocity measurements in vegetated channels.Journal of Hydraulic Engineering, 128(7), 664-673 (2002)
[7] Wu, Y., Falconer, R. A., and Struve, J. Mathematical modelling of tidal currents in mangroveforests. Environmental Modelling and Software, 16(1), 19-29 (2001)
[8] Huai, W. X., Han, J., Zeng, Y. H., An, X., and Qian, Z. H. Velocity distribution of flow with submergedflexible vegetations based on mixing length approach. Applied Mathematics and Mechanics(English Edition), 30(3), 343-351 (2009) DOI 10.1007/s10483-009-0308-1
[9] Petryk, S. and Bosmajian, G. Analysis of flow through vegetation. Journal of the HydraulicsDivision, 101(7), 871-884 (1975)
[10] Kouwen, N. Modern approach to design of grassed channels. Journal of Hydrology, 118(5), 733-743 (1992)
[11] Helmiö, T. Unsteady 1D flow model of compound channel with vegetated floodplains. Journal ofHydrology, 269(1-2), 89-99 (2002)
[12] Helmiö, T. Unsteady 1D flow model of a river with partly vegetated floodplains—application tothe Rhine River. Environmental Modelling and Software, 20(3), 361-375 (2005)
[13] Järvelä, J. Flow resistance of flexible and stiff vegetation: a flume study with natural plants.Journal of Hydrology, 269(1-2), 44-54 (2002)
[14] Stone, B. M. and Shen, H. T. Hydraulic resistance of flow in channels with cylindrical roughness.Journal of Hydraulic Engineering, 128(5), 500-506 (2002)
[15] Kutija, V. and Hong, H. T. M. A numerical model for assessing the additional resistance to flowintroduced by flexible vegetation. Journal of Hydraulic Research, 34(1), 99-114 (1996)
[16] Darby, S. E. Effect of riparian vegetation on flow resistance and flood potential. Journal of Hy-draulic Engineering, 125(5), 443-454 (1999)
[17] Vionnet, C. A., Tassi, P. A., and Martin-Vide, J. P. Estimates of flow resistance and eddy viscositycoefficients for 2D modelling on vegetated floodplains. Hydrological Processes, 18(25), 2907-2926(2004)
[18] Simoes, F. J. and Wang, S. S. Y. Three-dimensional modelling of compound channels with vegetatedflood plains. The 27th IAHR Congress on Environmental and Coastal Hydraulics: Protectingthe Aquatic Habitat (ed. Wang, S. S. Y.), ASCE, San Francisco, 809-814 (1997)
[19] Shimuzu, Y. and Tsujimoto, T. Suspended sediment concentration affected by organized motionnear vegetation zone. The 27th IAHR Congress on Environmental and Coastal Hydraulics:Protecting the Aquatic Habitat (ed. Wang, S. S. Y.), ASCE, San Francisco, 1384-1389 (1997)
[20] Fischer-Antze, T., Stoesser, T., Bates, P., and Olsen, N. R. B. 3D numerical modelling of openchannelflow with submerged vegetation. International Journal for Numerical Methods in Fluids,39(3), 303-310 (2001)
[21] Zhang, Z. T. and Su, X. H. Numerical model for flow motion with vegetation. Journal of Hydro-dynamics, 20(2), 172-178 (2008)
[22] Liu, C. and Shen, Y. M. Flow structure and sediment transport with impacts of aquatic vegetation.Journal of Hydrodynamics, 20(4), 461-468 (2008)
[23] Huai, W. X., Geng, C., Zeng, Y. H., and Yang, Z. H. Analytical solutions for transverse distributionsof stream-wise velocity in turbulent flow in rectangular channel with partial vegetation. Ap-plied Mathematics and Mechanics (English Edition), 32(4), 459-468 (2011) DOI 10.1007/s10483-011-1430-6
[24] Huai, W. X., Xu, Z. G., Yang, Z. H., and Zeng, Y. H. Two-dimensional analytical solutionfor a partially vegetated compound channel flow. Applied Mathematics and Mechanics (EnglishEdition), 29(8), 1077-1084 (2008) DOI 10.1007/s10483-008-0811-y
[25] Singh, V. and Bhallamudi, S. M. Conjunctive surface-subsurface modelling of overland flow. Ad-vances in Water Resources, 21(7), 567-579 (1998)
[26] Yakirevich, A., Borisov, V., and Sorek, S. A quasi three-dimensional model for flow and transportin unsaturated and saturated zones: 1. implementation of the quasi two-dimensional case.Advances in Water Resources, 21(8), 679-689 (1998)
[27] Cartwright, N., Jessen, O. J., and Nielsen, P. Application of a coupled ground-surface water flowmodel to simulate periodic groundwater flow influenced by a sloping boundary, capillarity, andvertical flows. Environmental Modelling and Software, 21, 770-778 (2005)
[28] Erduran, K. S., Macalister, C. R., and Kutija, V. Finite volume solution to integrated shallowsurface-saturated groundwater flow. International Journal for Numerical Methods in Fluids, 9(7),763-783 (2005)
[29] Thompson, J. R., S?renson, H. R., Gavin, H., and Refsgaard, A. Application of the coupledMIKE SHE/MIKE 11 modelling system to a lowland wet grassland in southeast England. Journalof Hydrology, 293(1-4), 151-179 (2004)
[30] Erduran, K. S. An Integrated Model for Complex Flow Simulations: COMSIM, Ph.D. dissertation,University of Newcastle upon Tyne (2001)
[31] Roe, P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal ofComputational Physics, 43(2), 357-372 (1981)
[32] Brufau, P., V′azquez-Cend′on, M. E., and Garcia-Navarro, P. A numerical model for the floodingand drying of irregular domains. International Journal for Numerical Methods in Fluids, 39(3),247-275 (2002)
[33] Abbott, M. B. and Minns, A.W. Computational Hydraulics, 2nd ed., Ashgate, Connecticut (1998)
[34] Timoshenko, S. Strength of Materials, Part 1: Elementary Theory and Problems, Van NostrandCompany, New York (1955)
[35] Shaw, E. M. Hydrology in Practice, 3rd ed., Chapman and Hall, London (1994)
[36] Anderson, M. P. and Woessner, W. W. Applied Groundwater Modelling: Simulation of Flow andAdvective Transport, Academic Press, New York (1992)
[37] Rodi, W. Turbulence Models and Their Application in Hydraulics: A State-of-the-Art Review, 3rded., Rotterdam, the Netherlands (1993)