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A finite difference method for calculating surface waves in coastal zone

A finite difference method for calculating surface waves in coastal zone - Nonlinear problems on potential flows of an ideal fluid with a free surface in a bounded tank of finite depth are formulated in curvilinear coordinates. Finite difference methods for solving these problems on movable adaptive grids are discussed. Numerical modelling of the propagation of surface waves over the surface of the water in the ocean and in the coastal zone enjoys wide application In most papers devoted to this problem discrete models for calculating transformation of waves when they are propagating offshore are based on approximate mathematical models. Either linear and nonlinear shallow-water models or various versions of a more accurate, though more difficult to implement, nonlinearly dispersive model are employed [8,9,15,16, 23,26]. All these models as a rule neglect variations of the fluid parameters with depth. When waves approach the shore, nonlinearity in the wave propagation shows up most vividly. Vertical movements of the fluid in the coastal zone, especially near obstacles and structures, match or even exceed horizontal ones. The application of shallow-water models in the immediate vicinity of the shore can lead to significant errors and therefore more accurate mathematical models along with approximate models are required in conducting numerical experiments in the coastal http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Russian Journal of Numerical Analysis and Mathematical Modelling de Gruyter

A finite difference method for calculating surface waves in coastal zone

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0927-6467
eISSN
1569-3988
DOI
10.1515/rnam.1993.8.6.461
Publisher site
See Article on Publisher Site

Abstract

- Nonlinear problems on potential flows of an ideal fluid with a free surface in a bounded tank of finite depth are formulated in curvilinear coordinates. Finite difference methods for solving these problems on movable adaptive grids are discussed. Numerical modelling of the propagation of surface waves over the surface of the water in the ocean and in the coastal zone enjoys wide application In most papers devoted to this problem discrete models for calculating transformation of waves when they are propagating offshore are based on approximate mathematical models. Either linear and nonlinear shallow-water models or various versions of a more accurate, though more difficult to implement, nonlinearly dispersive model are employed [8,9,15,16, 23,26]. All these models as a rule neglect variations of the fluid parameters with depth. When waves approach the shore, nonlinearity in the wave propagation shows up most vividly. Vertical movements of the fluid in the coastal zone, especially near obstacles and structures, match or even exceed horizontal ones. The application of shallow-water models in the immediate vicinity of the shore can lead to significant errors and therefore more accurate mathematical models along with approximate models are required in conducting numerical experiments in the coastal

Journal

Russian Journal of Numerical Analysis and Mathematical Modelling – de Gruyter

Published: Jan 1, 1993

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