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Single-Grid Spectral Collocation for the Navier-Stokes Equations |
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| Authors: | BERNARDI CHRISTINE; CANUTO CLAUDIO; MADAY YVON; METIVET BRIGITTE |
| Institution: |
CNRS and Analyse Numérique , Université Pierre et Marie Curie Tour 55–65, 5è étage, 4 place Jussieu F-75252 Paris Cedex 05, France Università di Parma and Istituto di Analisi Numerica del CNR Corso C. Alberto, 5, I-27100 Pavia, Italia Université de Paris XII, ONERA and Analyse Numérique, Université Pierre et Marie Curie Tour 55–56, 5è étage, 5 place Jussieu F-75252 Paris Cedex 05, France EDF/DER/IMA/MMN 1 avenue du Général de Gaulle, F-92141 Clamart Cedex, France |
| Abstract: | The aim of the paper is to study a collocation spectral methodto approximate the Navier-Stokes equations: only one grid isused, which is built from the nodes of a Gauss-Lobatto quadratureformula, either of Legendre or of Chebyshev type. The convergenceis proved for the Stokes problem provided with inhomogeneusDirichlet conditions, then thoroughly analysed for the Navier-Stokesequations. The practical implementation algorithm is presented,together with numerical results. |
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