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**Further experiences with computing non-hydrostatic free-surface flows involving water waves.**
*(English)*
Zbl 1064.76075

Summary: A semi-implicit, staggered finite volume technique for non-hydrostatic, free-surface flow governed by incompressible Euler equations is presented that has a proper balance between accuracy, robustness and computing time. The procedure is intended to be used for predicting wave propagation in coastal areas. The splitting of the pressure into hydrostatic and non-hydrostatic components is utilized. To ease the task of discretization and to enhance the accuracy of the scheme, a vertical boundary-fitted co-ordinate system is employed, permitting more resolution near the bottom as well as near the free surface. The issue of the implementation of boundary conditions is addressed. As recently proposed by the present authors [ibid. 43, No. 1, 1–23 (2003; Zbl 1032.76645)], the Keller-box scheme for accurate approximation of frequency wave dispersion requiring a limited vertical resolution is incorporated. The both locally and globally mass conserved solution is achieved with the aid of a projection method in the discrete sense. An efficient preconditioned Krylov subspace technique to solve the discretized Poisson equation for pressure correction with an unsymmetric matrix is treated. Some numerical experiments to show the accuracy, robustness and efficiency of the proposed method are presented.

### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

86A05 | Hydrology, hydrography, oceanography |

### Keywords:

finite volume technique; incompressible Euler equations; Keller-box scheme; preconditioned Krylov subspace technique### Citations:

Zbl 1032.76645
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\textit{M. Zijlema} and \textit{G. S. Stelling}, Int. J. Numer. Methods Fluids 48, No. 2, 169--197 (2005; Zbl 1064.76075)

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