I.E Herrera–Díaz*¹, C. Couder–Castañeda², H. Ramírez León²

¹ Centro de Investigación en Matemáticas, AC. Jalisco S/N, Col. Valenciana, CP 36240 Guanajuato, Gto, Mexico. *E–mail: enriquehd@cimat.mx

² Mexican Petroleum Institute, Eje Central Lázaro Cárdenas 152, CP 07730, Mexico City, Mexico.

ABSTRACT

We develop a numerical model based on the mild–slope equation of water wave propagation over complex bathymetrys, taking into account the combined effects of refraction, diffraction and reflection due to protection structures. The numerical method was developed using a split proposed version of the mild–slope equation in elliptical form and solved by an implicit method in a finite volume mesh, this technique easily allows the modeling of the wave transformations caused by the protection structures in coastal waters, where industrial and other economic activities take place. Study cases controlled have been made and the results match very well with the reference solution. The capability and utility of the model for coastal areas are illustrated by its application to the breakwater of the Laguna Verde Nuclear Power Plant (LVNPP) and the protection structure of the Nautical Marine named "Los Ayala".

Keywords: near–shore, wave transformation, protection structures, implicit method.

RESUMEN

Se desarrolla un método numérico para resolver la ecuación de la pendiente suave, para el estudio de la propagación del oleaje en batimetrías complejas, tomando en cuenta los efectos combinados de la refracción, difracción y reflexión causados por estructuras de protección. El método numérico se basa en la descomposición de la ecuación de la pendiente suave en su forma elíptica para resolverla por un método implícito en volúmenes finitos. Esta técnica permite la modelación de las transformaciones del oleaje causadas por las estructuras de protección en aguas costeras, donde actividades industriales y recreativas tienen lugar. Casos de estudio controlados fueron hechos y los resultados coinciden con la solución de referencia. La capacidad y utilidad del modelo para aguas costeras es ilustrado con la aplicación al rompeolas de la Planta Nuclear de Laguna Verde y la estructura de protección en la Marina Náutica "Los Ayala".

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