Métodos de elementos finitos estabilizados para flujos de fluidos incompresibles

Unión EuropeaDirección General de Investigación Científica y Técnic

Oscillations due to the transport of microstructures

The aim of this paper is to report some improvements and some numerical tests of a model for convection of microstructures developed by McLaughlin, Papanicolaou and Pironneau ISLAM J. Appl. Math., 45 (1985), pp. 780-797]. This model was obtained by homogenization techniques. In particular, this paper gives a computational indication of the existence of oscillations in a macroscopic flow which evolves from an initial state with two well-separated length scales. This oscillatory behavior was formally predicted by McLaughlin et al. A simplified model including eddy viscosity terms is first obtained: This model is tested for a threedimensional Poiseuille flow in which the mean flow is one-dimensional. Direct simulations and the simulations of the model are compared and good agreement is obtained in the behavior of both the mean velocity field and the kinetic energy of the microstructure

Stabilization of a non standard FETI-DP mortar method for the Stokes problem

In a recent paper [E. Chacón Vera and D. Franco Coronil, J. Numer. Math. 20 (2012) 161–182.] a non standard mortar method for incompressible Stokes problem was introduced where the use of the trace spaces H1/2 and H1/2 00 and a direct computation of the pairing of the trace spaces with their duals are the main ingredients. The importance of the reduction of the number of degrees of freedom leads naturally to consider the stabilized version and this is the results we present in this work. We prove that the standard Brezzi–Pitkaranta stabilization technique is available and that it works well with this mortar method. Finally, we present some numerical tests to illustrate this behaviour.Ministerio de Ciencia e InnovaciónJunta de Andaluci

A variational finite element model for Large-Eddy simulations of turbulent flows

We introduce a new Large Eddy Simulation model in a channel, based on the projection on finite element spaces as filtering operation in its variational form, for a given triangulation {Th}h>0. The eddy viscosity is expressed in terms of the friction velocity in the boundary layer due to the wall, and is of a standard sub grid-model form outside the boundary layer. The mixing length scale is locally equal to the grid size. The computational domain is the channel without the linear sub-layer of the boundary layer. The no slip boundary condition (BC) is replaced by a Navier (BC) at the computational wall. Considering the steady state case, we show that the variational finite element model we have introduced, has a solution (vh, ph)h>0 that converges to a solution of the steady state Navier-Stokes Equation with Navier BC.Ministerio de Economía y Competitivida

Finite element discretization of the Stokes and Navier-Stokes equations with boundary conditions on the pressure

We consider the Stokes and Navier–Stokes equations with boundary conditions of Dirichlet type on the velocity on one part of the boundary and involving the pressure on the rest of the boundary. We write the variational formulations of such problems. Next we propose a finite element discretization of them and perform the a priori and a posteriori analysis of the discrete problem. Some numerical experiments are presented in order to justify our strategy.Ministerio de Economía e InnovaciónFondo Europeo de Desarrollo Regiona

A domain decomposition method derived from the Primal Hybrid Formulations for 2nd order elliptic problems

We consider the primal hybrid formulation for second order elliptic problems introduced by Raviart-Thomas and apply the classical iterative method of Uzawa to obtain a non overlapping domain decomposition method that converges geometrically with a mesh independent ratio. The proposed method connects with the Finite Element Tearing and Interconnecting (FETI) method proposed by Farhat-Roux and collaborators. In this research work we use the detailed work on domains with corners developed by Grisvard [6], which clarifies the situation of cross-points, and the direct computation of the duality H−1/2 − H1/2 using the H1/2 scalar product; therefore no consistency error appears