Méthode des éléments spectraux

Résumé

Dans la solution numérique des équations aux dérivées partielles, un sujet en mathématiques, la méthode des éléments spectraux est une formulation de la méthode des éléments finis qui utilise des degrés élevés de polynômes par morceaux comme fonctions de base. Historique La méthode des éléments spectraux a été introduite dans un article de 1984 par A. T. Patera. Notes et références Bibliographie *A. T. Patera. A spectral element method for fluid dynamics - Laminar flow in a channel expansion. Journal of Computational Physics, 54:468--488, 1984. Catégorie:Mécanique des milieux continus Elements spectraux

Source officielle

https://fr.wikipedia.org/wiki/M%C3%A9thode_des_%C3%A9l%C3%A9ments_spectraux

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Publications associées (58)

Publications associées

Chargement

Personnes associées (7)

Personnes associées

Chargement

Unités associées (4)

Unités associées

Chargement

Concepts associés

Chargement

Cours associés (4)

Cours associés

Chargement

Séances de cours associées (8)

Séances de cours associées

Chargement

Stabilized spectral element methods for the simulation of viscoelastic flows

EPFL2002

Chargement

In this work we apply the discontinuous Galekin (dG) spectral element method on meshes made of simplicial elements for the approximation of the elastodynamics equation. Our approach combines the high accuracy of spectral methods, the geometrical flexibility of simplicial elements and the computational efficiency of dG methods. We analyze the dissipation, dispersion and stability properties of the resulting scheme, with a focus on the choice of different sets of basis functions. Finally, we apply the method on benchmark as well as realistic test cases.

Springer Verlag2016

Chargement

Simulation of flows of viscoelastic fluids at high Weissenberg number using a filter-based stabilization of the spectral element method

Michel Deville, Nicolas Fietier, Azadeh Jafari

The challenge for computational rheologists is to develop efficient and stable numerical schemes in order to obtain accurate numerical solutions for the governing equations at values of practical interest of the Weissenberg number. One of the associated problems for numerical simulation of viscoelastic fluids is that the accuracy of the results when approaching critical values at which numerical instabilities occur is very low and refining the mesh proved to be not very helpful. In order to investigate the numerical instability generation a comprehensive study about the growth of spurious modes with time evolution, mesh refinement, boundary conditions and Weissenberg number or any other affected parameters is performed on the planar Poiseuille channel flow. To get rid of these spurious modes the filter based stabilization of spectral element methods proposed by Boyd (1998) [1] is applied. This filter technique is very useful to eliminate spurious modes for one element decomposition, while in the case of multi-element configuration, the performance of this technique is not ideal. Since the performance of filter-based stabilization of spectral element acts very well for one element decomposition, a possible remedy to solve the associated problem of multi-element decomposition is mesh-transfer technique which means: first mapping the multi-element configuration to one element configuration, applying filter-based stabilization technique to this new topology and hereafter transferring the filtered variables to the original configuration. This way of implementing filtering is very useful for the Oldroyd-B fluids when a moderate number of grid points is used. (C) 2011 Elsevier Ltd. All rights reserved.

2012

Chargement