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An augmented mixed finite element method for the Navier-Stokes equations with variable viscosity

Opened Access An augmented mixed finite element method for the Navier-Stokes equations with variable viscosity

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Autor: Camaño Valenzuela, Jessika
Gatica Pérez, Gabriel Nibaldo
Oyarzúa Vargas, Ricardo
Tierra Chica, Giordano
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2016
Publicado en: SIAM Journal on Numerical Analysis, 54 (2), 1069-1092.
Tipo de documento: Artículo
Resumen: A new mixed variational formulation for the Navier–Stokes equations with constant density and variable viscosity depending nonlinearly on the gradient of velocity, is proposed and analyzed here. Our approach employs a technique previously applied to the stationary Boussinesq problem and to the Navier-Stokes equations with constant viscosity, which consists firstly of the introduction of a modified pseudostress tensor involving the diffusive and convective terms, and the pressure. Next, by using an equivalent statement suggested by the incompressibility condition, the pressure is eliminated, and in order to handle the nonlinear viscosity, the gradient of velocity is incorporated as an auxiliary unknown. Furthermore, since the convective term forces the velocity to live in a smaller space than usual, we overcome this difficulty by augmenting the variational formulation with suitable Galerkin-type terms arising from the constitutive and equilibrium equations, the aforementioned relatio...
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Cita: Camaño Valenzuela, J., Gatica Pérez, G.N., Oyarzúa Vargas, R. y Tierra Chica, G. (2016). An augmented mixed finite element method for the Navier-Stokes equations with variable viscosity. SIAM Journal on Numerical Analysis, 54 (2), 1069-1092.
Tamaño: 2.035Mb
Formato: PDF

URI: http://hdl.handle.net/11441/42634

DOI: http://dx.doi.org/10.1137/15M1013146

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