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

A new meshless local B-spline basis functions-FD method for two-dimensional heat conduction problems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

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

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
DOI
10.1108/HFF-05-2013-0169
Publisher site
See Article on Publisher Site

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.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Mar 2, 2015

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