92 research outputs found
On the approximation of turbulent fluid flows by the Navier-Stokes- equations on bounded domains
The Navier-Stokes- equations belong to the family of LES (Large Eddy
Simulation) models whose fundamental idea is to capture the influence of the
small scales on the large ones without computing all the whole range present in
the flow. The constant is a regime flow parameter that has the
dimension of the smallest scale being resolvable by the model. Hence, when
, one recovers the classical Navier-Stokes equations for a flow of
viscous, incompressible, Newtonian fluids. Furthermore, the
Navier-Stokes- equations can also be interpreted as a regularization of
the Navier-Stokes equations, where stands for the regularization
parameter.
In this paper we first present the Navier-Stokes- equations on
bounded domains with no-slip boundary conditions by means of the Leray
regularization using the Helmholtz operator. Then we study the problem of
relating the behavior of the Galerkin approximations for the
Navier-Stokes- equations to that of the solutions of the Navier-Stokes
equations on bounded domains with no-slip boundary conditions. The Galerkin
method is undertaken by using the eigenfunctions associated with the Stokes
operator. We will derive local- and global-in-time error estimates measured in
terms of the regime parameter and the eigenvalues. In particular, in
order to obtain global-in-time error estimates, we will work with the concept
of stability for solutions of the Navier-Stokes equations in terms of the
norm
The Initial Value Problem for the Equations of Magnetohydrodynamic Type in Non-Cylindrical Domain
Sin resume
Optimal error estimates of the penalty finite element method for micropolar fluids equations
An optimal error estimate of the numerical velocity, pressure and angular velocity, is proved for the fully discrete penalty finite element method of the micropolar equations, when the parameters ², ∆t and h are sufficiently small. In order to obtain above we present the time discretization of the penalty micropolar equation which is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Micropolar equation is based on a finite elements space pair (Hh, Lh) which satisfies some approximate assumption
Global solution of nematic liquid crystals models
We prove existence of a global weak solution for a nematic liquid crystal problem by means of a penalization method using a simplified Ericksen-Leslie model and a new compactness property for the gradient of the director field
Optimal control problem for the generalized bioconvective flow
In this work, we consider an optimal control problem for the generalized bioconvective flow, which is a well known model to describe the convection caused by the concentration of upward swimming microorganisms in a fluid. Firstly, we study the existence and uniqueness of weak solutions for this model, moreover we prove the existence of the optimal control and we establish the minimum principle by using Dubovitskii-Milyutin’s formalism.DGI-MEC BFM2003- 06446CGCI MECD-DGU Brazil/Spain 117/06FONDECYT 103094
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