A Conformal Decomposition Finite Element Method (CDFEM) is developed for modeling material death. Material death is used to model the continuous removal of material that exceeds a prescribed temperature. CDFEM allows for the moving front to move through the material without having to conform to the finite element geometry. The method is tested using 2-dimensional simulations of a 1-dimensional problem with an analytical solution. CDFEM is shown to be optimal for the chosen discretization with first order convergence in time and second order convergence in space. In comparison, a traditional element death algorithm does not converge at all on unstructured meshes. A correction is proposed for remedying this problem, resulting in first order convergence for traditional element death in space and time.
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A Conformal Decomposition Finite Element Method for Material Death
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Noble, DR. "A Conformal Decomposition Finite Element Method for Material Death." Proceedings of the ASME 2012 Heat Transfer Summer Conference collocated with the ASME 2012 Fluids Engineering Division Summer Meeting and the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels. Volume 2: Heat Transfer Enhancement for Practical Applications; Fire and Combustion; Multi-Phase Systems; Heat Transfer in Electronic Equipment; Low Temperature Heat Transfer; Computational Heat Transfer. Rio Grande, Puerto Rico, USA. July 8–12, 2012. pp. 1059-1063. ASME. https://doi.org/10.1115/HT2012-58464
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