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Boundary transfer operators in one‐way nesting schemes for heat flow problems

Evgeny Shavelzon (Department of Aerospace Engineering, Technion, Israel Institute of Technology, Haifa, Israel)
Dan Givoli (Department of Aerospace Engineering, Technion, Israel Institute of Technology, Haifa, Israel)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 15 May 2009

188

Abstract

Purpose

The interaction of a global model (GM) and a local (regional) model (LM) of heat flow is considered under the framework of so‐called “one‐way nesting”. In this framework, the GM is constructed in a large domain with coarse discretization in space and time, while the LM is set in a small subdomain with fine discretization.

Design/methodology/approach

The GM is solved first, and its results are then used via some boundary transfer operator (BTO) on the GM–LM interface in order to solve the LM. Past experience in various fields of application has shown that one has to be careful in the choice of BTO to be used on the GM–LM interface, since this choice affects both the stability and accuracy of the computational scheme. Here the problem is first theoretically analyzed for the linear heat equation, and stable BTOs are identified. Then numerical experiments are performed with one‐way nesting in a two‐dimensional channel for heat flow with and without radiation emission and linear reaction, using four different BTOs.

Findings

Among other conclusions, it is shown that the “negative Robin” BTO is unstable, whereas the Dirichlet, Neumann and “positive Robin” BTO are all stable. It is also shown that in terms of accuracy, the Neumann and “positive Robin” BTOs should be preferred over the Dirichlet BTO.

Originality/value

This study may be the first step in analyzing BTO accuracy and stability for more general atmospheric systems.

Keywords

Citation

Shavelzon, E. and Givoli, D. (2009), "Boundary transfer operators in one‐way nesting schemes for heat flow problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 19 No. 3/4, pp. 352-373. https://doi.org/10.1108/09615530910938326

Publisher

:

Emerald Group Publishing Limited

Copyright © 2009, Emerald Group Publishing Limited

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