The RIDE model: an enhanced computer program for wave transformation

Abstract A wave transformation model (RIDE) was enhanced to include the process of wave breaking energy dissipation in addition to water wave refraction, diffraction, reflection, shoaling, bottom friction, and harbor resonance. The Gaussian Elimination with partial Pivoting (GEP) method for a banded matrix equation and a newly developed bookkeeping procedure were used to solve the elliptic equation. Because the bookkeeping procedure changes the large computer memory requirements into a large hard-disk-size requirement with a minimum number of disk I/O, the simple and robust GEP method can be used in personal computers to handle realistic applications. The computing time is roughly proportional to N 1.7 , where N is the number of grid points in the computing domain. Because the GEP method is capable of solving many wave conditions together (limited by having the same wave period, no bottom friction and no breaking), this model is very efficient compared to iteration methods when simulating some of the wave transformation process.

[1]  Bin Li,et al.  A generalized conjugate gradient model for the mild slope equation , 1994 .

[2]  T. Hsu,et al.  A parabolic equation extended to account for rapidly varying topography , 2001 .

[3]  Alan G. Davies,et al.  Surface-wave propagation over sinusoidally varying topography , 1984, Journal of Fluid Mechanics.

[4]  Using the Gaussian Elimination Method for Large Banded Matrix Equations , 1997 .

[5]  P. G. Chamberlain,et al.  The modified mild-slope equation , 1995, Journal of Fluid Mechanics.

[6]  Jose M. Grassa,et al.  Comparison of Wave Refraction and Diffraction Models , .

[7]  Stanisław Ryszard Massel,et al.  Ocean Surface Waves: Their Physics and Prediction , 1996 .

[8]  David W. Wang,et al.  Wave Transformation Near Virginia Coast: the "Halloween" Northeaster , 1995 .

[9]  Changhoon Lee,et al.  Time-dependent equations for wave propagation on rapidly varying topography , 1997 .

[10]  Bin Li,et al.  An evolution equation for water waves , 1994 .

[11]  H. Hwung,et al.  A Wave Transformation Model for Harbor Planning , 1997 .

[12]  Tai-Wen Hsu,et al.  Comparison of wave refraction and diffraction models , 2000 .

[13]  James T. Kirby,et al.  PARABOLIC WAVE COMPUTATIONS IN NON-ORTHOGONAL COORDINATE SYSTEMS , 1988 .

[14]  Chiang C. Mei,et al.  Long Wave Excitation in Harbours - An Analytical Study. , 1973 .

[15]  Jack Dongarra,et al.  LINPACK Users' Guide , 1987 .

[16]  Ivar G. Jonsson,et al.  EXPERIMENTAL AND THEORETICAL INVESTIGATIONS IN AN OSCILLATORY TURBULENT BOUNDARY LAYER , 1976 .

[17]  A study of using parabolic model to describe wave breaking and wide‐angle wave incidence , 2000 .

[18]  Per A. Madsen,et al.  An efficient finite-difference approach to the mild-slope equation , 1987 .

[19]  J. Kirby.  Rational approximations in the parabolic equation method for water waves , 1986 .

[20]  Yvon Ouellet,et al.  A new kind of nonlinear mild-slope equation for combined refraction-diffraction of multifrequency waves , 1997 .

[21]  A. C. Radder,et al.  On the parabolic equation method for water-wave propagation , 1978, Journal of Fluid Mechanics.

[22]  James T. Kirby,et al.  A note on parabolic radiation boundary conditions for elliptic wave calculations , 1989 .

[23]  G. Copeland,et al.  A practical alternative to the “mild-slope” wave equation , 1985 .

[24]  D. Porter,et al.  Extensions of the mild-slope equation , 1995, Journal of Fluid Mechanics.

[25]  Ge Wei,et al.  Solution of the mild-slope wave problem by iteration , 1991 .

[26]  James T. Kirby,et al.  Higher‐order approximations in the parabolic equation method for water waves , 1986 .

[27]  A. C. Radder,et al.  Verification of numerical wave propagation models for simple harmonic linear water waves , 1982 .

[28]  Akira Watanabe,et al.  Numerical Modeling of Nearshore Wave Field Under Combined Refraction, Diffraction and Breaking , 1986 .

[29]  Robert A. Dalrymple,et al.  Models for very wide-angle water waves and wave diffraction. Part 2. Irregular bathymetry , 1989, Journal of Fluid Mechanics.

[30]  K. Anastasiou,et al.  Efficient elliptic solvers for the mild-slope equation using the multigrid technique , 1992 .

[31]  H. Walker.  Implementation of the GMRES method using householder transformations , 1988 .