Applied Mathematics and Mechanics

, Volume 34, Issue 6, pp 721–730 | Cite as

Vertical two-dimensional non-hydrostatic pressure model with single layer

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Abstract

The vertical two-dimensional non-hydrostatic pressure models with multiple layers can make prediction more accurate than those obtained by the hydrostatic pres-sure assumption. However, they are time-consuming and unstable, which makes them unsuitable for wider application. In this study, an efficient model with a single layer is developed. Decomposing the pressure into the hydrostatic and dynamic components and integrating the x-momentum equation from the bottom to the free surface can yield a horizontal momentum equation, in which the terms relevant to the dynamic pressure are discretized semi-implicitly. The convective terms in the vertical momentum equation are ignored, and the rest of the equation is approximated with the Keller-box scheme. The velocities expressed as the unknown dynamic pressure are substituted into the continuity equation, resulting in a tri-diagonal linear system solved by the Thomas algorithm. The validation of solitary and sinusoidal waves indicates that the present model can provide comparable results to the models with multiple layers but at much lower computation cost.

Key words

vertical two-dimensional model non-hydrostatic pressure single layer Thomas algorithm wave 

Chinese Library Classification

O352 

2010 Mathematics Subject Classification

76M20 
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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ling Kang (康 玲)
    • 1
  • Xiao-ming Guo (郭晓明)
    • 1
  1. 1.School of Hydropower and Information EngineeringHuazhong University of Science and TechnologyWuhanP. R. China

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