Multilevel Methods for the Simulation of Turbulence: A Simple Model

✍ Scribed by Roger Temam

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 330 KB
• Volume: 127
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0177

✦ Synopsis

Our aim in this article is to present for a very simple modelnamely a pair of ordinary coupled differential equations-some of the features of the multilevel numerical methods which have been y(0) ϭ y 0 , z(0) ϭ z 0 .

(2) introduced recently for the numerical simulation of turbulent flows.

The two components of this simple differential system are intended to represent the large and small scale components of a flow. We Here y and z play the same role respectively as the low show that many new numerical schemes can be introduced by and high frequency components of the flow (e.g., of the treating differently the small and large scale components; also difvelocity vector). The important features of the matrix in ferent time steps can be used for these two components. The stabil-

(1) is that its eigenvalues are O(1) and O(1/), Ͼ 0 small; ity analysis which we conduct for this simple model shows that these new multilevel schemes can produce a substantial saving in the linear coupling terms ( y Ϫ z and z Ϫ y terms) are not computing time, although the stability analysis leads sometime to important and in fact are not present in the related case counterintuitive conclusions. The error analysis for this model of Fourier and spectral discretizations.

will be conducted elsewhere. Also the reader is referred to the For this very simple system and also for the associated articles quoted below (in particular, [8, 10]) for the utilization of similar multilevel schemes for the Navier-Stokes equations linear system obtained by dropping the nonlinear terms, themselves.