Open Access

ARTICLE

The MLPG(5) for the Analysis of Transient Heat Transfer in the Frequency Domain

by L. Godinho¹, D. Dias-da-Costa²

1 CICC, Dept. Civil Engineering, University of Coimbra, Portugal.
2 INESCC, University of Coimbra, and Dept. Civil Engineering, University of Coimbra, Portugal; School of Civil Engineering, The University of Sydney, NSW2006, Australia.

Computer Modeling in Engineering & Sciences 2013, 96(5), 293-316. https://doi.org/10.3970/cmes.2013.096.293

Abstract

Transient heat conduction problems can be dealt with using different numerical approaches. In some recent papers, a strategy to tackle these problems using a frequency domain formulation has been presented and successfully applied associated to methods such as the BEM. Here a formulation of the meshless local Petrov-Galerkin (MLPG) is developed and presented to allow the analysis of such problems. The proposed formulation makes use of the RBF-based version of the MLPG and employs the Heaviside step function as the test function, leading to the so-called MLPG(5). In addition, the method is associated with a visibility criterion to allow the correct selection of neighbouring nodes for interpolation. This criterion greatly simplifies the incorporation of discontinuities, such as cracks or holes, into the numerical model, and allows handling more complex geometries. The model is verified and application examples are presented, illustrating the usefulness of the method in the analysis of realistic configurations.

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