Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T17:54:56.572Z Has data issue: false hasContentIssue false
  • English
  • Français

Using Fictitious Time Integration Method to Study Wave Propagation Over Arbitrary Bathymetry

Published online by Cambridge University Press:  01 May 2013

J.-Y. Chang ,
C.-C. Tsai  and
T.-W. Hsu
J.-Y. Chang
Affiliation:
Department of Business Administration, Tainan University of Technology, Tainan, Taiwan 71002, R.O.C.
C.-C. Tsai*
Affiliation:
Department of Marine Environmental Engineering, National Kaohsiung Marine University, Kaohsiung City, Taiwan 81157, R.O.C.
T.-W. Hsu
Affiliation:
Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
*Corresponding author (tsaichiacheng@mail.nkmu.edu.tw)
Get access

Abstract

In this study, the fictitious time integration method (FTIM) is applied to investigate wave propagation over an arbitrary bathymetry with measured uncertainty. The FTIM is used to convert the higher-order elliptic mild-slope equation (EMSE) into a FTIM like EMSE (FTIMEMSE). It has the advantage to describe wave transformation from deep water to shallow water region in a large coastal area with numerical efficiency. The validity of the noise resistance for the measured uncertainty of the bathymetry is also studied. In addition, typical examples for waves propagating over an elliptic shoal rest on a horizontal and sloping bottom is presented. It is concluded that the FTIM is robust in the numerical stability and capable of against the noise of the measurement.

Keywords

Fictitious time integration methodMild slope equationWater wave
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 3 , September 2013 , pp. 551 - 558
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Berkhoff, J. C. W., “Computation of Combined Refraction-Diffraction,” 13th International Conference on Coastal Engineering, pp. 471–490 (1972).Google Scholar
2.Booij, N., “A Note on the Accuracy of the Mild-Slope Equation,” Coastal Engineering, 7, pp. 191–203 (1983).CrossRefGoogle Scholar
3.Kirby, J. T., “Higher-Order Approximations in the Parabolic Equation Method for Water Waves,” Journal of Geopphysical Research, 91, pp. 933–952 (1986).Google Scholar
4.Chamberlain, P. G. and Porter, D., “The Modified Mild-Slope Equation,” Journal of Fluid Mechanics, 291, pp. 393–407 (1995).Google Scholar
5.Massel, S. R., “Extended Refraction-Diffraction Equation for Surface Waves,” Coastal Engineering, 19, pp. 97–126 (1993).Google Scholar
6.Suh, K. D., Lee, C. and Park, W. S., “Time-Dependent Equations for Wave Propagation on Rapidly Varying Topography,” Coastal Engineering, 32, pp. 91–117 (1997).CrossRefGoogle Scholar
7.Lee, C., Kim, G. and Suh, K. D., “Extended Mild-Slope Equation for Random Waves,” Coastal Engineering, 48, pp. 277–287 (2003).Google Scholar
8.Lee, C., Kim, G. and Suh, K. D., “Comparison of Time-Dependent Extended Mild-Slope Equations for Random Waves,” Ocean Engineering, 53, pp. 311–318 (2006).Google Scholar
9.Chandrasekera, C. N. and Cheung, K. F., “Extended Linear Refraction-Diffraction Model,” Journal of Waterway, Port, Coastal, and Ocean Engineering, 123, pp. 280–286 (1997).CrossRefGoogle Scholar
10.Chen, W., Panchang, V. and Demirbilek, Z., “On the Modeling of Wave-Current Interaction Using the Elliptic Mild-Slope Wave Equation,” Ocean Engineering, 32, pp. 2135–2164 (2005).Google Scholar
11.Panchang, V., Chen, W., Xu, B., Schlenker, K., Demirbilek, Z. and Okihiro, M., “Exterior Bathy-metric Effects in Elliptic Harbor Wave Models,” Journal of Waterway, Port, Coastal, and Ocean Engineering, 126, pp. 71–78 (2000).CrossRefGoogle Scholar
12.Copeland, G. J. M., “A Practical Alternative to the “Mild-Slope” Wave Equation,” Coastal Engineering, 9, pp. 125–149 (1985).Google Scholar
13.Lee, C., Sun Park, W., Cho, Y.-S. and Doug Suh, K., “Hyperbolic Mild-Slope Equations Extended to Account for Rapidly Varying Topography,” Coastal Engineering, 34, pp. 243–257 (1998).Google Scholar
14.Li, B., “An Evolution Equation for Water Waves,” Coastal Engineering, 23, pp. 227–242 (1994).Google Scholar
15.Hsu, T.-W. and Wen, C.-C., “A Parabolic Equation Extended to Account for Rapidly Varying Topography,” Ocean Engineering, 28, pp. 1479–1498 (2001).Google Scholar
16.Hsu, T.-W., Lin, T.-Y., Wen, C.-C. and Ou, S.-H., “A Complementary Mild-Slope Equation Derived Using Higher-Order Depth Function for Waves Obliquely Propagating on Sloping Bottom,” Physics of Fluids, 18, http://dx.doi.org/10.1063/L2337734 (2006).Google Scholar
17.Davies, A. G. and Heathershaw, A. D., “Surface-Wave Propagation over Sinusoidally Varying Topography,” Journal of Fluid Mechanics, 144, pp. 419–443 (1984).Google Scholar
18.Williams, R. G., Darbyshire, J., Holmes, P. and Berkhoff, J. C. W., “Wave Refraction and Diffraction in a Caustic Region: A Numerical Solution and Experimental Validation,” ICE Proceedings, 69, pp. 635–649 (1980).Google Scholar
19.Reniers, A. J. H. M. and Battjes, J. A., “A Laboratory Study of Longshore Currents over Barred and Non-Barred Beaches,” Coastal Engineering, 30, pp. 1–21 (1997).Google Scholar
20.Liu, C. S. and Atluri, S. N., “A Novel Time Integration Method for Solving a Large System of NonLinear Algebraic Equations,” Computer Modeling in Engineering & Sciences, 31, pp. 71–84 (2008).Google Scholar
21.Liu, C. S., “A Lie-Group Shooting Method for Simultaneously Estimating the Time-Dependent Damping and Stiffness Coefficients,” Computer Modeling in Engineering & Sciences, 27, pp. 137–150 (2008).Google Scholar
22.Liu, C. S., “The Lie-Group Shooting Method for Nonlinear Two-Point Boundary Value Problems Exhibiting Multiple Solutions,” Computer Modeling in Engineering & Sciences, 5, pp. 55–84 (2008).Google Scholar
23.Liu, C. S. and Atluri, S. N., “A Novel Fictitious Time Integration Method for Solving the Discretized Inverse Sturm-Liouville Problems, for Specified Eigenvalues,” Computer Modeling in Engineering & Sciences, 36, pp. 261–285 (2008).Google Scholar
24.Liu, C. S., “A Fictitious Time Integration Method for Solving M-Point Boundary Value Problems,” Computer Modeling in Engineering & Sciences, 39, pp. 125–154 (2009).Google Scholar
25.Liu, C. S. and Atluri, S. N., “A Fictitious Time Integration Method for the Numerical Solution of the Fredholm Integral Equation and for Numerical Differentiation of Noisy Data, and Its Relation to the Filter Theory,” Computer Modeling in Engineering & Sciences, 41, pp. 243–261 (2009).Google Scholar
26.Liu, C. S. and Atluri, S. N., “A Fictitious Time Integration Method (FTIM) for Solving Mixed Complementarity Problems with Applications to Non-Linear Optimization,” Computer Modeling in Engineering & Sciences, 34, pp. 155–178 (2008).Google Scholar
27.Liu, C. S., “A Fictitious Time Integration Method for Two-Dimensional Quasilinear Elliptic Boundary Value Problems,” Computer Modeling in Engineering & Sciences, 33, pp. 179–198 (2008).Google Scholar
28.Liu, C. S., “A Fictitious Time Integration Method for a Quasilinear Elliptic Boundary Value Problem, Defined in an Arbitrary Plane Domain,” Computers Materials & Continua, 11, pp. 15–32 (2009).Google Scholar
29.Ku, C. Y., Yeih, W. C., Liu, C. S. and Chi, C. C., “Applications of the Fictitious Time Integration Method Using a New Time-Like Function,” Computer Modeling in Engineering & Sciences, 43, pp. 173–190 (2009).Google Scholar
30.Chang, C. W., “A Fictitious Time Integration Method for Multi-Dimensionalbackward Heat Conduction Problems,” Computers, Materials & Continua, 19, pp. 285–314 (2010).Google Scholar
31.Chang, C. W., “A Fictitious Time Integration Method for Multi-Dimensional Backward Wave Problems,” Computers, Materials & Continua, 21, pp. 87–105 (2011).Google Scholar
32.Radder, A. C., “On the Parabolic Equation Method for Water-Wave Propagation,” Journal of Fluid Mechanics, 95, pp. 159–176 (1979).CrossRefGoogle Scholar
33.Hsu, T.-W., Lan, Y.-J., Wang, Y.-H. and Tsai, C.-Y., “Using Finite-Element Method to Simulate Wave Transformations in Surf Zone,” Journal of Engineering Mechanics, 131, pp. 1214–1217 (2005).Google Scholar
34.Hsu, T.-W., Chang, J.-Y., Lan, Y.-J., Lai, J.-W. and Ou, S.-H., “A Parabolic Equation for Wave Propagation over Porous Structures,” Coastal Engineering, 55, pp. 1148–1158 (2008).Google Scholar
35.Vincent, C. L. and Briggs, M. J., “Refraction-Diffraction of Irregular Waves over a Mound,” Journal of Waterway, Port, Coastal, and Ocean Engineering, 115, pp. 269–284 (1989).CrossRefGoogle Scholar