Special Section Articles

Coupling of One-Dimensional and Two-Dimensional Hydrodynamic Models Using an Immersed-Boundary Method

[+] Author and Article Information
Ning Zhang

Department of Engineering,
McNeese State University,
Lake Charles, LA 70609
e-mail: nzhang@mcneese.edu

Puxuan Li, Anpeng He

Department of Engineering,
McNeese State University,
Lake Charles, LA 70609

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 23, 2013; final manuscript received October 7, 2013; published online February 28, 2014. Assoc. Editor: Elias Balaras.

J. Fluids Eng 136(4), 040907 (Feb 28, 2014) (7 pages) Paper No: FE-13-1046; doi: 10.1115/1.4025676 History: Received January 23, 2013; Revised October 07, 2013

Numerical simulations of flooding events through rivers and channels require coupling between one-dimensional (1D) and two-dimensional (2D) hydrodynamic models. The rivers and channels are relatively narrow, and the widths could be smaller than the grid size used in the background 2D model. The shapes of the rivers and channels are often complex and do not necessarily coincide with the grid points. The coupling between the 1D and 2D models are challenging. In this paper, a novel immersed-boundary (IB) type coupling is implemented. Using this method, no predetermined linking point is required, nor are the discharge boundary conditions needed to be specified on the linking points. The linkage will be dynamically determined by comparing the water levels in the 1D channel and the surrounding dry cell elevations on the 2D background. The linking-point flow conditions, thus, can be dynamically calculated by the IB type implementation. A typical problem of the IB treatment, which is the forming of the nonsmooth zigzag shaped boundary, has not been observed with this method. This coupling method enables more realistic and accurate simulations of water exchange between channels and dry lands during a flooding event.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Bates, P. D., and Hervouet, J. M., 1999, “A New Method for Moving Boundary Hydrodynamic Problems in Shallow Water,” Proc. R. Soc. London, Ser. A, 455, pp. 3107–3128. [CrossRef]
Defina, A., 2000, “Two-Dimensional Shallow Flow Equation for Partially Dry Areas,” Water Resour. Res., 36(11), pp. 3251–3264. [CrossRef]
Rungo, M., and Olesen, K. W., 2003, “Combined 1- and 2-Dimensional Flood Modeling,” Proceedings of the 4th Iranian Hydraulic Conference, Shiraz, Iran, October. 21–23.
Center for Louisiana Inland Water Studies, 2011, “Improvement, Utilization, and Assessment of Chenier Plain models for the Southwest Coastal Louisiana Feasibility Study—Calibration and Validation Results for the Chenier Plain Circulation Model,” Institute of Coastal Ecology and Engineering, University of Louisiana at Lafayette, Technical Report.
DHI Software, 2007, MIKE FLOOD User Manual, DHI Software, Hørsholm, Denmark.
Zhang, N., and Zheng, Z. C., 2007, “An Improved Direct-Forcing Immersed-Boundary Method for Finite Difference Applications,” J. Comput. Phys., 221(1), pp. 250–268. [CrossRef]
Peskin, C. S., 1972, “Flow Patterns Around Heart Valves: A Numerical Method,” J. Comput. Phys., 10, pp. 252–271. [CrossRef]
Balaras, E., and Yang, J., 2005, “Nonboundary Conforming Methods for Large-Eddy Simulations of Biological Flows,” ASME J. Fluids Eng., 127, pp. 851–857. [CrossRef]
Yang, J., and Balaras, E., 2006, “An Embedded-Boundary Formulation for Large-Eddy Simulation of Turbulent Flows Interacting With Moving Boundaries,” J. Comput. Phys., 215, pp. 12–40. [CrossRef]
Ying, X., Khan, A. A., and Wang, S. S., 2004, “Upwind Conservative Scheme for the Saint Venant Equations,” J. Hydraul. Eng., 130, pp. 977–987. [CrossRef]
Crowe, C. T., Elger, D. F., Williams, B. C., and Roberson, J. A., 2009, Engineering Fluid Mechanics, 9th ed., Wiley, New York.
Uhlmann, M., 2005, “An Immersed Boundary Method With Direct Forcing for the Simulation of Particulate Flows,” J. Comput. Phys., 209(2), pp. 448–476. [CrossRef]
Vanella, M., and Balaras, E., 2009, “A Moving-Least-Squares Reconstruction for Embedded-Boundary Formulation,” J. Comput. Phys., 228(18), pp. 6617–6628. [CrossRef]
Fadlun, E. A., Verzicco, R., Orlandi, P., and Mohd-Yusof, J., 2000, “Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations,” J. Comput. Phys., 161, pp. 35–60. [CrossRef]
Zhang, N., Zheng, Z. C., and Yadagiri, S., 2011, “A Hydrodynamic Simulation for the Circulation and Transport in Coastal Watersheds,” Comput. Fluids, 47(1), pp. 178–188. [CrossRef]
Zheng, Z. C., and Zhang, N., 2002, “A Hydrodynamics Simulation for Mobile Bay Circulation,” Proceedings of the International Mechanical Engineering Congress and Exposition, New Orleans, LA.
Zhang, N., Kee, D., and Li, P., 2013, “Investigation of the Impacts of Gulf Sediments on Calcasieu Ship Channel and Surrounding Water Systems,” Comput. Fluids, 77, pp. 125–133. [CrossRef]
Zhang, N., Li, P., and He, A., 2012, “Coupling of 1-D and 2-D Hydrodynamic Model Using Immersed-Boundary Method,” Proceedings of the ASME Fluids Engineering Summer Meeting, Puerto Rico, July 8–12.


Grahic Jump Location
Fig. 1

Illustration of the IB structure [6]

Grahic Jump Location
Fig. 2

Water surface elevation at t = 30 s compared to the 1D dam break case in the literature

Grahic Jump Location
Fig. 3

Topography of the test case

Grahic Jump Location
Fig. 4

Water surface elevation in the channel at t = 5000 s, comparison among different IB resolutions

Grahic Jump Location
Fig. 5

Water surface elevation in the channel at t = 5000 s, comparison among different grid resolutions

Grahic Jump Location
Fig. 6

L2-norms of water surface elevation results in Fig. 5

Grahic Jump Location
Fig. 7

The histories of total flooded mass, comparison among different grid resolutions

Grahic Jump Location
Fig. 8

L2-norms of total flooded mass results in Fig. 7

Grahic Jump Location
Fig. 9

Water-surface elevation contours with velocity vector fields, at (a) t = 2500 s and (b) t = 5000 s

Grahic Jump Location
Fig. 10

Histories showing the mass conservation: (a) histories of water mass exchange rate between 1D channel and 2D background and (b) history of the total mass which entered the domain compared to the total mass on the domain




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In