An efficient and flexible computational model for solving the mild slope equation

Themildslopeequationisusedtodescribewavepropagatinginthenearshoreregion.Inthispaper,thefinitedifferencemethod isusedtodiscretizethegoverningellipticequationandthediscretizedlinearequationissolvedusingGPBiCG(m,n)method.Two cases of wave propagating are used to test the model, and reasonable agreements have been achieved. It is shown that the present algorithm: GPBiCG(m,n)withaflexibleanddiverseform,hasafastandrelativelyrobust convergencerate,andcanbeefficiently and economically run in either the linear or nonlinear wave model and easily used to a complicated region. D 2004 Elsevier B.V. All rights reserved.

[1]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

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

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

[4]  C. Vuik.  Solution of the discretized incompressible Navier‐Stokes equations with the GMRES method , 1993 .

[5]  Yonghong,et al.  Efficient Elliptic Solver for the Mild Slope Equation Using BI-CGSTAB Method , 2000 .

[6]  Seiji Fujino,et al.  GPBiCG(m, l): a hybrid of BiCGSTAB and GPBiCG methods with efficiency and robustness , 2002 .

[7]  Shao-Liang Zhang,et al.  GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems , 1997, SIAM J. Sci. Comput..

[8]  K. Anastasiou,et al.  MODELLING OF WAVE PROPAGATION IN THE NEARSHORE REGION USING THE MILD SLOPE EQUATION WITH GMRES‐BASED ITERATIVE SOLVERS , 1996 .

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

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

[11]  J. Berkhoff,et al.  Computation of Combined Refraction — Diffraction , 1972 .

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

[13]  K. Anastasiou,et al.  An efficient computational model for water wave propagation in coastal regions , 1998 .

[14]  Vijay Panchang,et al.  Combined refraction-diffraction of short-waves in large coastal regions , 1988 .

[15]  Robert A. Dalrymple,et al.  Verification of a parabolic equation for propagation of weakly-nonlinear waves , 1984 .