Solution of a low Prandtl number natural convection benchmark by a local meshless method

Gregor Kosec (Laboratory for Parallel and Distributed Computing, Jožef Stefan Institute, Ljubljana, Slovenia and Laboratory for Multiphase Processes, University of Nova Gorica, Nova Gorica, Slovenia)
Božidar Šarler (Laboratory for Multiphase Processes, University of Nova Gorica, Nova Gorica, Slovenia and Laboratory for Advanced Materials Systems, Centre of Excellence for Biosensorics, Automation and Process Control, Solkan, Slovenia)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 4 January 2013

Abstract

Purpose

The purpose of this paper is to present the solution of a highly nonlinear fluid dynamics in a low Prandtl number regime, typical for metal‐like materials, as defined in the call for contributions to a numerical benchmark problem for 2D columnar solidification of binary alloys. The solution of such a numerical situation represents the first step towards understanding the instabilities in a more complex case of macrosegregation.

Design/methodology/approach

The involved temperature, velocity and pressure fields are represented through the local approximation functions which are used to evaluate the partial differential operators. The temporal discretization is performed through explicit time stepping.

Findings

The performance of the method is assessed on the natural convection in a closed rectangular cavity filled with a low Prandtl fluid. Two cases are considered, one with steady state and another with oscillatory solution. It is shown that the proposed solution procedure, despite its simplicity, provides stable and convergent results with excellent computational performance. The results show good agreement with the results of the classical finite volume method and spectral finite element method.

Originality/value

The solution procedure is formulated completely through local computational operations. Besides local numerical method, the pressure velocity is performed locally also, retaining the correct temporal transient.

Keywords

Citation

Kosec, G. and Šarler, B. (2013), "Solution of a low Prandtl number natural convection benchmark by a local meshless method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 1, pp. 189-204. https://doi.org/10.1108/09615531311289187

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Publisher

:

Emerald Group Publishing Limited

Copyright © 2013, Emerald Group Publishing Limited

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