We propose a semisecret in time semi-implicit numerical scheme for the infinite Prandtl model for convection. Besides the usual finite time convergence, this scheme enjoys the additional highly desirable feature that the stationary statistical properties of the scheme converge to those of the infinite Prandtl number model at vanishing time stop. One of the key characteristics of the scheme is that it preserves the dissipativity of the infinite Prandtl number model uniformly in terms of the time stop. So far as wo know, this is the first rigorous result on convergence of stationary statistical properties of numerical schemes for infinite dimensional dissipative complex systems. © 2008 Society for Industrial and Applied Mathematics.


Mathematics and Statistics

Keywords and Phrases

Infinite Prandtl Number Model; Nusselt Number; Stationary Statistical Property; Uniformly Dissipativo Scheme

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

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Publication Date

01 Dec 2008