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Research Papers: Flows in Complex Systems

Implementation of an Infinite-Height Levee in CaFunwave Using an Immersed-Boundary Method

[+] Author and Article Information
Adam Oler

Department of Chemical, Civil,
and Mechanical Engineering,
McNeese State University,
Lake Charles, LA 70609

Ning Zhang

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

Steven R. Brandt

Center for Computation
and Technology,
Louisiana State University,
Baton Rouge, LA 70808

Qin Chen

Center for Computation and Technology,
Louisiana State University,
Baton Rouge, LA 70808

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 13, 2015; final manuscript received April 13, 2016; published online July 15, 2016. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 138(11), 111103 (Jul 15, 2016) (9 pages) Paper No: FE-15-1833; doi: 10.1115/1.4033490 History: Received November 13, 2015; Revised April 13, 2016

Numerical simulations of storm-surge–wave actions on coastal highways and levees are very important research topics for coastal engineering. In a large-scale region hydrodynamic model, highways and levees are often complicated in geometry and much smaller in size compared to the grid spacing. The immersed-boundary method (IBM) allows for those complicated geometries to be modeled in a less expensive way. It can allow very small geometries to be modeled in a large-scale simulation, without requiring them to be explicitly on the grid. It can also allow for complicated geometries not collocated on the grid points. CaFunwave is a project that uses the Cactus Framework for modeling a solitary coastal wave impinging on a coastline and is the wave solver in this research. The IBM allows for a levee with different geometries to be implemented on a simple Cartesian grid in the CaFunwave package. The IBM has not been often used previously for these types of applications. Implementing an infinite-height levee using the IBM into the Cactus project CaFunwave involves introducing immersed-boundary (IB) forcing terms into the standard two-dimensional (2D) depth-averaged shallow water equation set. These forcing terms cause the 2D solitary wave to experience a virtual force at the grid points surrounding the IB levee. In this paper, the levee was implemented and tested using two different IBMs. The first method was a feedback-forcing method, which proved to be more effective at modeling the levee than the second method, the direct-forcing method. In this study, the results of the two methods are presented and discussed. The effect of levee shape on the flow is also investigated and discussed in this paper.

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References

Figures

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Fig. 1

Geometry of levees and relative locations of physical features: (a) the entire domain and (b) the zoom-in view showing the size of mesh used comparing to the size of the island

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Fig. 6

Elevation time history 0.9 m in front of the levee

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Fig. 7

Elevation time history 2.9 m in front of the levee

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Fig. 8

Water elevation plots on Y = 10.6 m: (a) t = 1.898 s, (b) t = 3.828 s, and (c) t = 7.04 s

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Fig. 9

Water elevation contours between concave (left) and convex (right) IB levees at times (a) 1.892 s, (b) 3.828 s, and (c) 7.04 s

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Fig. 5

Water elevation contours, comparing between IB levee and HC levee at different times: (a) 1.892 s, (b) 3.828 s, and (c) 7.04 s

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Fig. 4

The L2-norm versus the grid number in the x direction of the domain, for the data in Fig. 2

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Fig. 3

Time histories of water elevation at a location 2.9 m in front of the IB levee

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Fig. 2

Water elevation plot on y = 10.6 m

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Fig. 10

Water elevation time histories at 0.9 m in front of the IB levees

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Fig. 11

Water elevation time histories at 2.9 m in front of the IB levees

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