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Application of the RBF collocation method to transient coupled thermoelasticity

Boštjan Mavrič (Institute of Metals and Technology, Ljubljana, Slovenia)
Božidar Šarler (Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia and Institute of Metals and Technology, Ljubljana, Slovenia)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 2 May 2017

153

Abstract

Purpose

In this study, the authors aim to upgrade their previous developments of the local radial basis function collocation method (LRBFCM) for heat transfer, fluid flow, electromagnetic problems and linear thermoelasticity to dynamic-coupled thermoelasticity problems.

Design/methodology/approach

The authors solve a thermoelastic benchmark by considering a linear thermoelastic plate under thermal and pressure shock. Spatial discretization is performed by a local collocation with multi-quadrics augmented by monomials. The implicit Euler formula is used to perform the time stepping. The system of equations obtained from the formula is solved using a Newton–Raphson algorithm with GMRES to iteratively obtain the solution. The LRBFCM solution is compared with the reference finite-element method (FEM) solution and, in one case, with a solution obtained using the meshless local Petrov–Galerkin method.

Findings

The performance of the LRBFCM is found to be comparable to the FEM, with some differences near the tip of the shock front. The LRBFCM appears to converge to the mesh-converged solution more smoothly than the FEM. Also, the LRBFCM seems to perform better than the MLPG in the studied case.

Research limitations/implications

The performance of the LRBFCM near the tip of the shock front appears to be suboptimal because it does not capture the shock front as well as the FEM. With the exception of a solution obtained using the meshless local Petrov–Galerkin method, there is no other high-quality reference solution for the considered problem in the literature yet. In most cases, therefore, the authors are able to compare only two mesh-converged solutions obtained by the authors using two different discretization methods. The shock-capturing capabilities of the method should be studied in more detail.

Originality/value

For the first time, the LRBFCM has been applied to problems of coupled thermoelasticity.

Keywords

Acknowledgements

We would like to thank the authors of Zheng et al. (2015) for kindly providing us with their MLPG solution to the benchmark problem. The research presented in this paper has been made possible by a Young Researcher grant from the Slovenian Ministry of Higher Education, Science and Sport (BM), programme P0-0501-0782, project L2-5667, sponsored by the Slovenian Grant Agency and the companies IMPOL Slovenska Bistrica and Štore – Steel (BŠ).

Citation

Mavrič, B. and Šarler, B. (2017), "Application of the RBF collocation method to transient coupled thermoelasticity", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 5, pp. 1064-1077. https://doi.org/10.1108/HFF-03-2016-0110

Publisher

:

Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited

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