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Einstein-Euler equations for matter spacetimes with Gowdy symmetry

Philippe G. LeFloch (2008/2009)

Séminaire Équations aux dérivées partielles

We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T 3 . Given an arbitrary initial data set, we establish the existence of a globally hyperbolic future development and we provide a global foliation of this spacetime in terms of a geometrically defined time-function coinciding with the area of the orbits of the symmetry group. This allows us to construct matter spacetimes with weak regularity which admit, both, impulsive...

Ekman boundary layers in rotating fluids

Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L 2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.

Ekman boundary layers in rotating fluids

Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.

Enabling numerical accuracy of Navier-Stokes-α through deconvolution and enhanced stability

Carolina C. Manica, Monika Neda, Maxim Olshanskii, Leo G. Rebholz (2011)

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

We propose and analyze a finite element method for approximating solutions to the Navier-Stokes-alpha model (NS-α) that utilizes approximate deconvolution and a modified grad-div stabilization and greatly improves accuracy in simulations. Standard finite element schemes for NS-α suffer from two major sources of error if their solutions are considered approximations to true fluid flow: (1) the consistency error arising from filtering; and (2) the dramatic effect of the large pressure error on the...

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