Indian Society for Heat and Mass Transfer

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Proceedings of the 25th National and 3rd International ISHMT-ASTFE Heat and Mass Transfer Conference (IHMTC-2019)

ISSN: 2688-7231 (Online)

Stabilised Meshless Local Petrov Galerkin Method for Heat Conduction

Rituraj Singh
Department of communication systems, Jozef Stefan Institute, Slovenia

Abhishek Kumar Singh
Department of Mechanical and Industrial Engineering, IIT Roorkee

Krishna Mohan Singh
Department of Mechanical and Industrial Engineering, IIT Roorkee, 247667, India

DOI: 10.1615/IHMTC-2019.1220
pages 727-732


In this paper, we propose meshless local Petrov Galerkin method based on stabilised moving least-squares approximation. Standard moving least squares (MLS) approximation is unstable at higher grid resolutions. Reason of this instability is ill-conditioning of moment matrix in the MLS procedure. As an evaluation point moves away from the origin, the condition number of the moment matrix increases. Further, the condition number also increases with the decrement of grid size. In the current work, we presented performance of the stabilised MLS approximation in the MLPG method for heat conduction problem and found that it provides stability at higher grid resolution.

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