44 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
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
On an iterative method for approximate solutions of a generalized Boussinesq model
An iterative method is proposed for nding approximate solutions of an initial and boundary value problem for a nonstationary generalized Boussinesq model for thermally driven convection of fluids with temperature
dependent viscosity and thermal conductivity. Under certain conditions, it is
proved that such approximate solutions converge to a solution of the original
problem; moreover, convergence-rate bounds for the constructed approximate solutions are also obtained
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
Semi-Galerkin approximation and strong solutions to the equations of the nonhomogeneous asymmetric fluids
This paper analyzes an initial/boundary value problem for a system of equations modelling the nonstationary flow of a nonhomogeneous incompressible asymmetric (polar) fluid. Under conditions similar to those usually imposed to the nonhomogeneous 3D Navier-Stokes equations,
by using a spectral semi-Galerkin method, we prove the existence of a local in time strong solution. We also prove the uniqueness of the strong solution and some global existence results. Several estimates for the solutions and their approximations are given. These can be used to find useful error bounds of the Galerkin approximations.Dans ce papier, on analyse un problème de valeurs initiales et
valeurs aux limites pour un système d’équations aux dérivées
partielles qui modélise le flux instationnaire d’un fluide asymmétrique
incompressible non homogène. Sous des conditions similaires aux conditions usuellement imposées aux équations tridimensionelles de Navier-Stokes non homogènes, à l’aide d’une méthode de type semi-Galerkin, nous démontrons l’éxistence d’une solution forte locale en temps. On établit aussi l’unicité de solution forte et quelques résultats d’éxistence globale. Tous ces résultats reposent sur des estimations appropriées pour les solutions et leurs approximations qui permettent d’ailleurs d´eduire des estimations de l’erreur.Conselho Nacional de Desenvolvimento Científico e Tecnológico (Brasil)Fundação de Amparo à Pesquisa do Estado de São PauloDirección General de Enseñanza Superio
An optimal control problem for a generalized Boussinesq model: The time dependent case
We consider an optimal control problem governed by a system of nonlinear
partial differential equations modelling viscous incompressible flows submitted
to variations of temperature. We use a generalized Boussinesq approximation.
We obtain the existence of the optimal control as well as first order optimality
conditions of Pontryagin type by using the Dubovitskii-Milyutin formalism.Ministerio de Educación y CienciaConselho Nacional de Desenvolvimento Científico e TecnológicoFundação de Amparo à Pesquisa do Estado de São Paul
Existence and uniqueness of strong solutions for the incompressible micropolar fluid equations in domains of R3
We consider the initial boundary value problem for the system of equations describing the nonstationary flow of an incompressible micropolar fluid in a domain Ω of R3.Under hypotheses that are similar to the Navier-Stokes equations ones, by using an iterative scheme, we prove the existence and uniqueness of strong solution in Lp(Ω), for p > 3
Inclusiones diferenciales, matemática difusa y aplicaciones
En este trabajo diremos cómo se pueden modelar ciertos sistemas
tomados de la realidad que usan conceptos propios de la Matemática
Difusa (conjuntos, multifunciones e inclusiones diferenciales “fuzzy”).
Consideraremos problemas de valor inicial para inclusiones diferenciales
“fuzzy” y analizaremos la existencia de solución local. También nos
referiremos a la estabilidad de los puntos de equilibrio de las inclusiones
diferenciales “fuzzy”. Finalmente, mostraremos algunas aplicaciones de
este desarrollo a problemas que aparecen en Biología.Ministerio de Ciencia y TecnologíaConselho Nacional de Desenvolvimento Científico e Tecnológic
Una nota sobre la existencia de soluciones para ecuaciones diferenciales difusas
Varios trabajos relacionados con la existencia y unicidad de soluciones para ecuaciones diferenciales difusas son basados en que el problema de Cauchy es equivalente a una ecuación integral. Este hecho que también es verdadero en el contexto clásico, no es siempre verdadero en el contexto de ecuaciones diferenciales difusas donde la derivada es considerada en el sentido generalizado. Mostraremos algunos ejemplos simples para demostrar esto y discutiremos sobre nuevas soluciones para una ecuación diferencial difusa