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A multilayer method for the hydrostatic Navier-Stokes equations: a particular weak solution

Opened Access A multilayer method for the hydrostatic Navier-Stokes equations: a particular weak solution

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Autor: Fernández-Nieto, Enrique D.
Koné, E.H.
Chacón Rebollo, Tomás
Departamento: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Fecha: 2014
Publicado en: Journal Scientific Computing, 60(2), 408-437
Tipo de documento: Artículo
Resumen: In this work we present a mutilayer approach to the solution of non-stationnary 3D Navier-Stokes equations. We use piecewise smooth weak solutions. We approximate the velocity by a piecewise constant (in z) horizontal velocity and a linear (in z) vertical velocity in each layer, possibly discontinuous across layer interfaces. The multilayer approach is deduced by using the variational formulation and by considering a reduced family of test functions. The procedure naturally provides the mass and momentum interfaces conditions. The mass and momentum conservation across interfaces is formulated via normal flux jump conditions. The jump conditions associated to momentum conservation are formulated by means of an approximation of the vertical derivative of the velocity that appears in the stress tensor. We approximate the multilayer model for hydrostatic pressure, by using a PVM finite volume scheme and we present some numerical tests that show the main advantages of the model: it impro...
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Tamaño: 947.7Kb
Formato: PDF

URI: http://hdl.handle.net/11441/40720

DOI: 10.1007/s10915-013-9802-0

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