Time-averaged shallow water model: asymptotic derivation and numerical validation
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Time-averaged shallow water model: asymptotic derivation and numerical validationDate
2015Center/Dept./Entity
Universidade da Coruña. Departamento de Métodos Matemáticos e de RepresentaciónCitation
J.M. Rodríguez, R. Taboada-Vázquez, Time-averaged shallow water model: Asymptotic derivation and numerical validation, Journal of Mathematical Analysis and Applications, Volume 428, Issue 2, 15 August 2015, Pages 930-950, ISSN 0022-247X, http://dx.doi.org/10.1016/j.jmaa.2015.03.050.
Abstract
The objective of this paper is to derive, from the Navier-Stokes equations in a shallow domain,a new bidimensional shallow water model able to filter the high frequency oscillations that are produced, when the Reynolds number is increased, in turbulent ows. With this aim, the non-
dimensional Navier-Stokes equations are time-averaged, and then asymptotic analysis techniques have been used as in our previous works. The small non-dimensional parameter considered, "e", is the quotient between the typical depth of the basin and the typical horizontal length of the domain; and it is studied what happens when "e" becomes
small.
Once the new model has been justified, by the method of asymptotic expansions, we perform
some numerical experiments. The results of these experiments con rm that this new model is able to approximate analytical solutions of Navier-Stokes equations with more accuracy than classical shallow water models, when high frequency oscillations appear. To reach a given accuracy, the time
step for the new model can be much larger (even four hundred times larger) than the time step required for the classical models.
Keywords
Shallow waters
Asymptotic analysis
Reynolds averaged navier-stokes equations
Modelling
Aguas poco profundas
Augas pouco profundas
Ecuaciones de Navier-Stokes
Ecuacións de Navier-Stokes
Análisis asintótico
Análise asintótico
Modelación
Asymptotic analysis
Reynolds averaged navier-stokes equations
Modelling
Aguas poco profundas
Augas pouco profundas
Ecuaciones de Navier-Stokes
Ecuacións de Navier-Stokes
Análisis asintótico
Análise asintótico
Modelación
Editor version
Rights
Reconocimiento-NoComercial-SinObraDerivada 3.0 España