Spectral approximations of the Stokes problem by divergence-free functions

Pasquarelli, Franco; Quarteroni, Alfio; Sacchi-Landriani, G.

doi:10.1007/bf01061110

Cited by 16 publications

(6 citation statements)

References 8 publications

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“…We refer, in particular, to the method of Moser, Moin and Leonard (1983) and its extensions (see Pasquarelli, Quarteroni and Sacchi Landriani (1987) and Pasquarelli (1991)). Once UN is available, the problem is how to recover a pressure field PN with the same optimal accuracy.…”

Section: Approximation By Spectral Methods 319mentioning

confidence: 99%

Numerical Approximation of Partial Differential Equations

Quarteroni

Valli

1994

Springer Series in Computational Mathematics

1,468

1,496

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This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is one of its main features. Many kinds of problems are addressed. A comprehensive theory of Galerkin method and its variants, as well as that of collocation methods, are developed for the spatial discretization. These theories are then specified to two numerical subspace realizations of remarkable interest: the finite element method and the spectral method

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Section: Approximation By Spectral Methods 319mentioning

confidence: 99%

Numerical Approximation of Partial Differential Equations

Quarteroni

Valli

1994

Springer Series in Computational Mathematics

1,468

1,496

View full text Add to dashboard Cite

show abstract

“…The method presented here was first proposed by Moser, Moin & Leonard (1983) and is also presented by Canuto et al (1988); an extensive description of the numerical method is also given in Pasquarelli, Quateroni & Sacchi-Landriani (1987). The goal is to project the velocity field onto a base of spatial functions that each verify the boundary non-slip conditions at the walls, and the solenoidal property.…”

Section: Methodsmentioning

confidence: 99%

Direct numerical simulations of turbulence with confinement and rotation

Godeferd

Lollini

1999

J. Fluid Mech.

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The goal of this work is to analyse how solid body rotation affects forced turbulence enclosed within solid boundaries, and to compare it to results of the experiment performed by Hopfinger et al. (1982). In order to identify various mechanisms associated with rotation, confinement, and forcing, a numerical pseudo-spectral code is used for performing direct numerical simulations. The geometry is simplified with respect to the experimental one. First, we are able to reproduce the linear regime, as propagating inertial waves that undergo reflections at the walls. Second, the Ekman pumping phenomenon, proportional to the rotation rate, is identified in freely decaying turbulence, for which the evolution of the flow bounded by walls is compared to the evolution of unbounded homogeneous turbulence. Finally we introduce a local forcing on a plane in physical space, for simulating the effect of an oscillating grid, so that diffusive turbulence is created, and we examine the structuring of the flow under the combination of the linear and nonlinear mechanisms. A transition to an almost two-dimensional state is shown to occur between the region close to the forcing and an outer region in which vortices appear, the number of which depends on the Reynolds and Rossby numbers. In this region, the anisotropy of turbulence is examined, and the numerical predictions are shown to reproduce many of the most important features present in the experimental flow.

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“…For some applications of our results we refer the reader to F. Pasquarelli, A. Quarteroni and G. Sacchi Landriani [23]. In this section we consider the Legendre spectral approximation of the Stokes system between two cylinders.…”

Section: An Applicationmentioning

confidence: 99%