Meshless Local B-spline Collocation Method for Heat Conduction Problems with Spatially Non-homogeneous and Time Dependent Heat Sources

[+] Author and Article Information
Mas Irfan P. Hidayat

Department of Materials and Metallurgical Engineering Institut Teknologi Sepuluh Nopember Kampus ITS Keputih Sukolilo 60111 Surabaya, East Java, Indonesia

Bambang Ariwahjoedi

Department of Fundamental and Applied Science Universiti Teknologi PETRONAS Bandar Seri Iskandar 31750 Tronoh, Perak Darul Ridzuan, Malaysia

Setyamartana Parman

Department of Mechanical Engineering Universiti Teknologi PETRONAS Bandar Seri Iskandar 31750 Tronoh, Perak Darul Ridzuan, Malaysia

T. V. V. L. N. Rao

Department of Mechanical-Mechatronics Engineering The LNM Institute of Information Technology Jaipur 302031, Rajasthan, India

1Corresponding author.

ASME doi:10.1115/1.4036003 History: Received January 24, 2015; Revised January 19, 2017


This paper presents a new approach of meshless local B-spline based finite difference (FD) method for solving transient heat conduction problems in complex geometries with spatially non-homogeneous and time dependent heat sources. 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 for either field variable approximation or integration, hence truly meshless. Time integration is performed by using the Galerkin implicit scheme. Several transient heat conduction problems with non-uniform and localized heat sources having potential relevance in industrial applications are examined to demonstrate the efficacy of the present approach. Comparison of the method results with solutions from other numerical methods in literature is given. Good agreement with reference numerical methods is obtained and the presented new meshless local method is shown to be simple and accurate.

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