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.

References

References
1.
Defina
,
A.
,
2000
, “
Two-Dimensional Shallow Flow Equation for Partially Dry Areas
,”
Water Resour. Res.
,
36
(
11
), pp.
3251
3264
.
2.
Spall
,
R. E.
,
Addley
,
C.
, and
Hardy
,
T.
,
2001
, “
Numerical Analysis of Large, Gravel-Bed Rivers Using the Depth-Averaged Equations of Motion
,”
ASME
Paper No. FEDSM2001-18169.
3.
Casulli
,
V.
,
1990
, “
Semi-Implicit Finite Difference Methods for the Two-Dimensional Shallow Water Equations
,”
J. Comput. Phys.
,
86
(
1
), pp.
56
74
.
4.
Marian
,
M.
,
Meselhe
,
E. A.
,
Weber
,
L.
, and
Bradley
,
A. A.
,
2001
, “
Coupled Physical-Numerical Analysis of Flows in Natural Waterways
,”
J. Hydraul. Res.
,
39
(1), pp.
51
60
.
5.
Peskin
,
C. S.
,
1982
, “
The Fluid Dynamics of Heart Valves: Experimental, Theoretical and Computational Methods
,”
Annu. Rev. Fluid Mech.
,
14
(
1
), pp.
235
259
.
6.
Iaccarino
,
G.
, and
Verzicco
,
R.
,
2003
, “
Immersed Boundary Technique for Turbulent Flow Simulations
,”
ASME Appl. Mech. Rev.
,
56
(
3
), pp.
331
347
.
7.
Mittal
,
R.
, and
Iaccarino
,
G.
,
2005
, “
Immersed Boundary Methods
,”
Annu. Rev. Fluid Mech.
,
37
(
1
), pp.
239
261
.
8.
Kang
,
S.
,
2008
, “
An Improved Immersed Boundary Method for Computation of Turbulent Flows With Heat Transfer
,”
Ph.D. thesis
, Stanford University, Stanford, CA.
9.
Saiki
,
E. M.
, and
Biringen
,
S.
,
1996
, “
Numerical Simulation of a Cylinder in a Uniform Flow: Application of a Virtual Boundary Method
,”
J. Comput. Phys.
,
123
(
2
), pp.
450
465
.
10.
Goldstein
,
D.
,
Handler
,
R.
, and
Sirovich
,
L.
,
1993
, “
Modeling a No-Slip Flow Boundary With an External Force Field
,”
J. Comput. Phys.
,
105
(
2
), pp.
354
366
.
11.
Mohd-Yusof
,
J.
,
1996
, “
Interaction of Massive Particles With Turbulence
,” Ph.D. dissertation, Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY.
12.
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
(
1
), pp.
35
60
.
13.
Kim
,
J.
,
Kim
,
D.
, and
Choi
,
H.
,
2001
, “
An Immersed Boundary Finite-Volume Method for Three Dimensional Complex Flow Simulations
,”
J. Comput. Phys.
,
171
(
1
), pp.
132
150
.
14.
Palma
,
P. D.
,
Tullio
,
M. D.
,
Pascazio
,
G.
, and
Napolitano
,
M.
,
2006
, “
An Immersed-Boundary Method for Compressible Viscous Flows
,”
Comput. Fluids
,
35
(
7
), pp.
693
702
.
15.
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
.
16.
Zhang
,
N.
,
Li
,
P.
, and
He
,
A.
,
2014
, “
Coupling of One-Dimensional and Two-Dimensional Hydrodynamic Models Using an Immersed-Boundary Method
,”
ASME J. Fluids Eng.
,
136
(
4
), pp.
1
7
.
17.
Balaras
,
E.
, and
Yang
,
J.
,
2005
, “
Nonboundary Conforming Methods for Large-Eddy Simulations of Biological Flows
,”
ASME J. Fluids Eng.
,
127
(
5
), pp.
851
857
.
18.
Ha
,
T.
,
Shim
,
J.
,
Lin
,
P.
, and
Cho
,
Y.
,
2014
, “
Three-Dimensional Numerical Simulation of Solitary Wave Run-Up Using the IB Method
,”
Coastal Eng.
,
84
, pp.
38
55
.
19.
Ouro
,
P.
,
Cea
,
L.
,
Ramirez
,
L.
, and
Nogueira
,
X.
, “
An Immersed Boundary Method for Unstructured Meshes in Depth Averaged Shallow Water Models
,”
Int. J. Numer. Methods Fluids
(published online).
20.
Shi
,
F.
,
Kirby
,
J. T.
,
Harris
,
J. C.
,
Geiman
,
J. D.
, and
Grilli
,
S. T.
,
2012
, “
A High-Order Adaptive Time-Stepping TVD Solver for Boussinesq Modeling of Breaking Waves and Coastal Inundation
,”
Ocean Modell.
,
43–44
, pp.
36
51
.
21.
Chen
,
Q.
,
2006
, “
Fully Nonlinear Boussinesq-Type Equations for Waves and Currents Over Porous Beds
,”
J. Eng. Mech.
,
132
(
2
), pp.
220
230
.
22.
Chen
,
Q.
,
Kirby
,
J. T.
,
Dalrymple
,
R. A.
,
Shi
,
F.
, and
Thornton
,
E. B.
,
2003
, “
Boussinesq Modeling of Longshore Currents
,”
J. Geophys. Res.
,
108
(
C11
), p.
3362
.
23.
Chen
,
Q.
,
Dalrymple
,
R. A.
,
Kirby
,
J. T.
,
Kennedy
,
A. B.
, and
Haller
,
M. C.
,
1999
, “
Boussinesq Modeling of a Rip Current System
,”
J. Geophys. Res.
,
104
(
C9
), pp.
20617
20637
.
24.
Chen
,
Q.
,
Kirby
,
J. T.
,
Dalrymple
,
R. A.
,
Kennedy
,
A. B.
, and
Chawla
,
A.
,
2000
, “
Boussinesq Modeling of Wave Transformation, Breaking, and Runup. II: 2D
,”
Int. J. Waterw. Port Coastal Ocean Eng.
,
126
(
1
), pp.
48
56
.
25.
Kempe
,
T.
, and
Frohlich
,
J.
,
2012
, “
An Improved Immersed Boundary Method With Direct Forcing for the Simulation of Particle laden Flows
,”
J. Comput. Phys.
,
231
(
9
), pp.
3663
3684
.
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