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A new meshless local B-spline basis functions-FD method for two-dimensional heat conduction problems

Mas Irfan Purbawanto Hidayat (Department of Mechanical Engineering, Universiti Teknologi PETRONAS, Tronoh, Malaysia and Department of Materials and Metallurgical Engineering, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia)
Bambang Ariwahjoedi (Department of Fundamental and Applied Science, Universiti Teknologi PETRONAS, Tronoh, Malaysia)
Setyamartana Parman (Department of Mechanical Engineering, Universiti Teknologi PETRONAS, Tronoh, Malaysia)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 2 March 2015

Abstract

Purpose

The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction problems.

Design/methodology/approach

In the present method, any governing equations are discretized by B-spline approximation which is implemented in the spirit of FD technique using a local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighbouring nodal values based on B-spline interpolants. The set of neighbouring nodes are allowed to be randomly distributed thus enhanced flexibility in the numerical simulation can be obtained. The method requires no mesh connectivity at all for either field variable approximation or integration. Time integration is performed by using the Crank-Nicolson implicit time stepping technique.

Findings

Several heat conduction problems in complex domains which represent for extended surfaces in industrial applications are examined to demonstrate the effectiveness of the present approach. Comparison of the obtained results with solutions from other numerical method available in literature is given. Excellent agreement with reference numerical method has been found.

Research limitations/implications

The method is presented for 2D problems. Nevertheless, it would be also applicable for 3D problems.

Practical implications

A transient two dimensional heat conduction in complex domains which represent for extended surfaces in industrial applications is presented.

Originality/value

The presented new meshless local method is simple and accurate, while it is also suitable for analysis in domains of arbitrary geometries.

Keywords

Acknowledgements

This research work is supported by grant provided by Universiti Teknologi PETRONAS, which is gratefully acknowledged. The present authors are also grateful to the reviewers for their comments and suggestions which further improve the quality and presentation of this paper.

Citation

Hidayat, M.I.P., Ariwahjoedi, B. and Parman, S. (2015), "A new meshless local B-spline basis functions-FD method for two-dimensional heat conduction problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 2, pp. 225-251. https://doi.org/10.1108/HFF-05-2013-0169

Publisher

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Emerald Group Publishing Limited

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