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An upper bound on the attractor dimension of a 2D turbulent shear flow with a free boundary condition

Mahdi Boukrouche, Grzegorz Łukaszewicz (2005)

Banach Center Publications

We consider a free boundary problem of a two-dimensional Navier-Stokes shear flow. There exist a unique global in time solution of the considered problem as well as the global attractor for the associated semigroup. As in [1] and [2], we estimate from above the dimension of the attractor in terms of given data and the geometry of the domain of the flow. This research is motivated by a free boundary problem from lubrication theory where the domain of the flow is usually very thin and the roughness...

Analysis and finite element error estimates for the velocity tracking problem for Stokes flows via a penalized formulation

Konstantinos Chrysafinos (2004)

ESAIM: Control, Optimisation and Calculus of Variations

A distributed optimal control problem for evolutionary Stokes flows is studied via a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as ε → 0 is examined.

Analysis and finite element error estimates for the velocity tracking problem for Stokes flows via a penalized formulation

Konstantinos Chrysafinos (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A distributed optimal control problem for evolutionary Stokes flows is studied via a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as ε → 0 is examined. ...

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that guarantee...

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that...

Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension

Jan Prüss, Gieri Simonett (2009)

Banach Center Publications

The two-phase free boundary value problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. We extract the boundary symbol which is crucial for the dynamics of the free boundary and present an analysis of this symbol. Of particular interest are its singularities and zeros which lead to refined mapping properties of the corresponding operator.

Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling ν ( p , · ) → + ∞ as p → + ∞

M. Bulíček, Josef Málek, Kumbakonam R. Rajagopal (2009)

Czechoslovak Mathematical Journal

Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities...

Analysis of the hydrostatic approximation in oceanography with compression term

Tomás Chacón Rebollo, Roger Lewandowski, Eliseo Chacón Vera (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...

Analysis of the hydrostatic approximation in oceanography with compression term

Tomás Chacón Rebollo, Roger Lewandowski, Eliseo Chacón Vera (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...

Anisotropic mesh adaption: application to computational fluid dynamics

Simona Perotto (2005)

Bollettino dell'Unione Matematica Italiana

In this communication we focus on goal-oriented anisotropic adaption techniques. Starting point has been the derivation of suitable anisotropic interpolation error estimates for piecewise linear finite elements, on triangular grids in 2 ⁢ D . Then we have merged these interpolation estimates with the dual-based a posteriori error analysis proposed by R. Rannacher and R. Becker. As examples of this general anisotropic a posteriori analysis, elliptic, advection-diffusion-reaction and the Stokes problems...

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