An Explicit Solution with Correctors for the Green–Naghdi Equations

Autor:	Samer Israwi, Ayman Mourad
Rok vydání:	2013
Předmět:	Physics::Fluid Dynamics Nonlinear system Simultaneous equations General Mathematics Mathematical analysis Linear model Boussinesq approximation (water waves) Physics::Atmospheric and Oceanic Physics Mathematics
Zdroj:	Mediterranean Journal of Mathematics. 11:519-532
ISSN:	1660-5454 1660-5446
DOI:	10.1007/s00009-013-0356-z
Popis:	In this paper, the water waves problem for uneven bottoms in a highly nonlinear regime is studied. It is well known that, for such regimes, a generalization of the Boussinesq equations called the Green–Naghdi equations can be derived and justified when the bottom is variable (Lannes and Bonneton in Phys Fluids 21, 2009). Moreover, the Green–Naghdi and Boussinesq equations are fully nonlinear and dispersive systems. We derive here new linear asymptotic models of the Green–Naghdi and Boussinesq equations so that they have the same accuracy as the standard equations. We solve explicitly the new linear models and numerically validate the results.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4fc864e217ead8fc7214cb6a09e584b7 https://doi.org/10.1007/s00009-013-0356-z Zobrazit plný text záznamu Full text from SpringerLink