Revista Recursos Hdricos
Volume 32, Nmero 2, Novembro 2011

DOI: 10.5894/rh32n2-1
O texto deste artigo foi submetido para reviso e possvel publicao em Setembro de 2011, tendo sido aceite pela Comisso de Editores Cientficos Associados em Outubro de 2011. Este artigo parte integrante da Revista Recursos Hdricos, Vol. 32, N 2, 7-16, Novembro de 2011.

Equaes de Boussinesq com Caractersticas Dispersivas Melhoradas. Aplicaes

Boussinesq-type Equations with Improved Dispersion Characteristics. Applications

Jos Simo Antunes do Carmo¹

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1 - IMAR – Instituto do Mar – Universidade de Coimbra, Departamento de Engenharia Civil, Plo II da Universidade /// 3030-788 Coimbra, PORTUGAL /// Associado da APRH com o nmero 1226 /// jsacarmo@dec.uc.pt

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RESUMO: Neste trabalho desenvolvida uma nova aproximao das equaes clssicas de Boussinesq, com caractersticas dispersivas melhoradas, e utilizado um esquema numrico apropriado para a resoluo do sistema de equaes resultante.
Considerando um simples parmetro para ter em conta os efeitos dispersivos, a discretizao adoptada permite comparar resultados numricos de duas aproximaes matemticas destas equaes (Boussinesq clssico e com caractersticas dispersivas melhoradas) com a soluo analtica aproximada das equaes.
Entre os resultados apresentados neste trabalho, destacam-se comparaes de solues numricas de ondas geradas por presses mveis superfcie (casos tpicos de embarcaes) considerando trs funes de presso (duas listadas na literatura da especialidade e uma terceira proposta) e duas aproximaes das equaes (Boussinesq clssico e modelo com caractersticas dispersivas melhoradas).
O modelo numrico desenvolvido testado para uma embarcao com 15 m de comprimento, que se move num canal com 10 m de profundidade, a uma velocidade de 5.0 m/s e exerce uma presso superfcie de 4900 N/m2.

Palavras-chave: Equaes de tipo Boussinesq, caractersticas dispersivas melhoradas, presso mvel superfcie, ondas geradas por embarcaes.

ABSTRACT: In this work, a new approximation of the classical Boussinesq equations with improved dispersive characteristics is developed, along with an appropriate numerical scheme to solve the resulting system of equations.
Considering a single parameter to take into account the dispersive effects, the adopted discretization allow us to compare numerical results of two mathematical approximations (the classical Boussinesq and the improved model with additional terms of dispersive origin) with the approximate analytical solution of the equations.
Among the results presented in this paper, we highlight comparisons of numerical solutions of waves generated by a mobile pressure at the surface (typical cases of boats), considering three functions of pressure (two listed in the specialized literature and a proposal third one) and two approximations of the equations (the classical Boussinesq and the model with improved dispersive characteristics).
The numerical model is tested for a boat of 15 m in length, moving in a channel 10 m deep at a speed of 5.0 m/s, and exerting a pressure of 4900 N/m2 at the surface.

Keywords: Boussinesq-type equations, improved dispersive characteristics, mobile pressure at surface, boat generated waves.

 

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