An Augmented Mixed Finite Element Method for the Navier--Stokes Equations with Variable Viscosity
| Autor: | Gabriel N. Gatica, Jessika Camaño, Ricardo Oyarzúa, Giordano Tierra |
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| Rok vydání: | 2016 |
| Předmět: |
Numerical Analysis
Applied Mathematics Mathematical analysis 010103 numerical & computational mathematics Mixed finite element method Space (mathematics) 01 natural sciences Physics::Fluid Dynamics 010101 applied mathematics Computational Mathematics Viscosity Nonlinear system Tensor 0101 mathematics Navier–Stokes equations Constant (mathematics) Variable (mathematics) Mathematics |
| Zdroj: | SIAM Journal on Numerical Analysis. 54:1069-1092 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/15m1013146 |
| Popis: | 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 relation defining the additi... |
| Databáze: | OpenAIRE |
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