An Explicit Solution with Correctors for the Green–Naghdi Equations

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• 作者：Samer Israwi (1) (2)
  Ayman Mourad (1) (3)
  
• 关键词：35Q53 ; 35L99 ; 35C05 ; 65M99 ; Water waves ; Green–Naghdi and Boussinesq systems ; topography effect ; asymptotic model ; explicit solution ; numerical validation
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：11
• 期：2
• 页码：519-532
• 全文大小：
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• 作者单位：Samer Israwi (1) (2)
  Ayman Mourad (1) (3)
  
  1. Laboratory of Mathematics, EDST Lebanese University, Hadath, Lebanon
  2. Center for Research in Applied Mathematics and Statistics, Arts Sciences and Technology University in Lebanon (AUL), 113-7504, Beirut, Lebanon
  3. Department of Mathematics, Faculty of Science (I), Lebanese University, Hadath, Lebanon
  
• ISSN：1660-5454

文摘

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.