The aim of this research is the development of a space-time driscretization method based on Diffuse Approximation Meshless method. This method, devoted to transient heat transfer problems presenting high temporal discontinuities, avoids any Finite-Difference time stepping procedure. The space-time discretization proposed here seems to be convenient for continuous transient heat transfer. Nevertheless, for problems including temporal discontinuities, some spurious oscillations, whose amplitudes depend on source power, appear. A new weight function respecting the principle of causality, based on a modification of the involved node’s selection and a normalisation of the distances, is developed. The use of this new weight function both improves the accuracy and vanishes the oscillations. The method is validated by a source free transient heat transfer problem presenting convective exchanges. Then problems including a constant and a discontinuous heat source are solved. Temperatures fields obtained when using the classical weight function are closer to those obtained with a backward Finite Difference scheme when the heat source is continuous. In case of discontinuous sources, when using the classical weight function, temperature fields present some spurious oscillations which disappear when choosing the new one. The proposed method associated to a grid refinement procedure will lead to adaptive grids in space and/or time, independently.
- Heat Transfer Division
A Space-Time Meshless Method for Heat Transfer Problems With High Discontinuities
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Da Silva, A, Sophy, T, & Kribèche, A. "A Space-Time Meshless Method for Heat Transfer Problems With High Discontinuities." Proceedings of the ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology. Volume 4: Heat and Mass Transfer Under Extreme Conditions; Environmental Heat Transfer; Computational Heat Transfer; Visualization of Heat Transfer; Heat Transfer Education and Future Directions in Heat Transfer; Nuclear Energy. Minneapolis, Minnesota, USA. July 14–19, 2013. V004T14A002. ASME. https://doi.org/10.1115/HT2013-17018
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