The incompressible Navier—Stokes equations

Quartapelle, L.

doi:10.1007/978-3-0348-8579-9_1

Cited by 82 publications

(136 citation statements)

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“…We worked with the equations of motion in their biharmonic form (1)- (3) rather than the more traditional streamfunction-vorticity formulation in order to avoid (a) inversion of the Poisson operator, and (b) difficulties arising from the coupling between the stream function and vorticity [12]. These are associated with the peculiar nature of the boundary conditions for the stream function • and the initial conditions on the vorticity w, which lacks boundary conditions [13]. In the biharmonic formulation the specification of both Dirichlet and Neumann boundary conditions for • poses no difficulty because both are required to supplement the fourthorder elliptic operator _74 present in Eq.…”

Section: 0x104mentioning

confidence: 99%

Confined states in large-aspect-ratio thermosolutal convection

1998

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Section: 0x104mentioning

confidence: 99%

Confined states in large-aspect-ratio thermosolutal convection

1998

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“…Quartapelle [17] pour une revue de ces techniques. La version qui nous intéresse ici est la version incrémentale, qui consisteà rendre explicite la pressionà l'étape de convection-diffusion età calculer l'incrément de pressionà l'étape de projection.…”

Section: Introductionunclassified

Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale

Guermond

1999

ESAIM: M2AN

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Abstract. The Navier-Stokes equations are approximated by means of a fractional step, ChorinTemam projection method; the time derivative is approximated by a three-level backward finite difference, whereas the approximation in space is performed by a Galerkin technique. It is shown that the proposed scheme yields an error of O(δt 2 + h l+1 ) for the velocity in the norm of l 2 (L 2 (Ω) d ), where l ≥ 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of projection schemes based on the incremental pressure correction is of O(δt 2 ) independent of the approximation order of the velocity time derivative.Résumé. Leséquations de Navier-Stokes sont approchées en temps par une schéma de différentiation rétrograde d'ordre deux et une technique de pas fractionnaire du type projection de Chorin-Temam ; l'approximation spatiale est réalisée par une technique de Galerkin. On montre qu'en temps fini, le schéma est d'ordre O(δt 2 + h l+1 ) pour la vitesse dans la norme l 2 (L 2 (Ω) d ), où l ≥ 1 est le degré polynomial d'approximation de la vitesse. On montre aussi que l'erreur de fractionnement des schémas de projection basés sur une correction de pression incrémentale est d'ordre O(δt 2 ), que l'approximation de la dérivée temporelle de la vitesse soit d'ordre un ou d'ordre deux.

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“…We refer to Appendix B in [13] for more details on how to decouple the 3D vector equations in spherical coordinates.…”

Section: Vector Equationsmentioning

confidence: 99%

Efficient Spectral-Galerkin Methods IV. Spherical Geometries

Shen¹

1999

SIAM J. Sci. Comput.

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Abstract. Fast spectral-Galerkin algorithms are developed for elliptic equations on the sphere. The algorithms are based on a double Fourier expansion and have quasi-optimal (optimal up to a logarithmic term) computational complexity. Numerical experiments indicate that they are significantly more efficient and/or accurate when compared with the algorithms based on spherical harmonics and on finite difference. Extensions to problems in spherical layers and to vector equations are also discussed.

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The incompressible Navier—Stokes equations

Cited by 82 publications

References 0 publications

Confined states in large-aspect-ratio thermosolutal convection

Confined states in large-aspect-ratio thermosolutal convection

Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale

Efficient Spectral-Galerkin Methods IV. Spherical Geometries

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