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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...

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

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...

Entrée-sortie dans un tourbillon

Guy Wallet (1986)

Annales de l'institut Fourier

On étudie un champ de vecteurs lent-rapide de R 3 nommé tourbillon pour lequel on démontre l’existence d’une fonction entrée-sortie.

Équation anisotrope de Navier-Stokes dans des espaces critiques.

Marius Paicu (2005)

Revista Matemática Iberoamericana

We study the tridimensional Navier-Stokes equation when the value of the vertical viscosity is zero, in a critical space (invariant by the scaling). We shall prove local in time existence of the solution, respectively global in time when the initial data is small compared with the horizontal viscosity.

Equations of magnetohydrodynamics of compressible fluid: Periodic solutions

Milan Štědrý, Otto Vejvoda (1985)

Aplikace matematiky

The authors prove the global existence and exponential stability of solutions of the given system of equations under the condition that the initial velocities and the external forces are small and the initial density is not far from a constant one. If the external forces are periodic, then solutions periodic with the same period are obtained. The investigated system of equations is a bit non-standard - for example the displacement current in the Maxwell equations is not neglected.

Equilibrium confocal textures in a smetic-A cell

Epifanio G. Virga, Jean-Baptiste Fournier (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study the textures of smectic-A liquid crystals consisting in curved, but stricdy equidistant lamellae. Assuming translational symmetry, we can generate them from a single curve. The free energy is a non-trivial functional of it. We learn how to derive the equilibrium equation for this curve, when the texture is confined between two parallel plates, which exert a weak anchoring on the orientation of the lamellae, but do not interfere direcdy with their position. Finally, we describe an instability...

Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes

Martin Vohralík (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the lowest-order Raviart–Thomas mixed finite element method for second-order elliptic problems on simplicial meshes in two and three space dimensions. This method produces saddle-point problems for scalar and flux unknowns. We show how to easily and locally eliminate the flux unknowns, which implies the equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. The matrix of the final linear system is sparse, positive...

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