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.

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Fig. 1

Illustration of the IB structure [6]

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Fig. 2

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

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Fig. 3

Topography of the test case

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Fig. 4

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

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Fig. 5

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

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Fig. 6

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

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Fig. 7

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

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Fig. 8

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

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Fig. 9

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

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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



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