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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v7.i1.60
pages 41-53

Multiscale Implications of the Inverse Rapid Energy Deposition Problem

Sam G. Lambrakos
Computational Multiphysics Systems Laboratory, Code 6394, Center for Computational Material Science, Naval Research Laboratory, Washington DC 20375, USA
John G. Michopoulos
Head Code 6394, FASME Computational Multiphysics Systems Lab Naval Research Laboratory Washington DC 20375

ABSTRAKT

The inverse energy deposition problem represents a particular subclass of the more general inverse heat conduction problem, where certain features that are associated with upstream-to-downstream spatial weighting of the temperature field diffusion pattern dominate. The present paper focuses on the case of rapid energy deposition processes, where it is shown that the influence of windage can be correlated with the extremely strong filtering of spatial and temporal structure within the associated diffusion pattern. This strong filtering tends to establish conditions where system identification, or in particular, reconstruction of detailed features of the energy source, based on data-driven inverse analysis is not well posed. Similarly, the strong filtering conditions associated with very rapid energy deposition imply consequences with respect to qualitative analysis using numerical simulations based on basic principles or the direct problem approach. That is to say, any experiment or basic theoretical information that is available concerning the coupling of energy into a spatial region of interest from a surface or interface, that is, the site of deposition, will be difficult to correlate with experimental observations of the associated energy diffusion pattern. Finally, it has been established that the primary implication of the analysis and simulations is that rapid energy deposition processes should be characterized by two distinctly separate scales for both spatial and temporal structures. The results of the analysis presented here indicate that the inverse rapid energy deposition problem requires a formulation with respect to system identification and parameterization that should be cast in terms of two separate sets of parameters. One should represent energy source characteristics on spatial and temporal scales commensurate with that of thermal diffusivity within the material. The other parameter set should represent energy source characteristics on spatial and temporal scales commensurate with those of surface phenomena.

REFERENZEN

  1. Ozisik, M. N. and Orlande, H. R. B., Inverse Heat Transfer, Fundamentals and Applications.

  2. Kurpisz, K. and Nowak, A. J., Inverse Thermal Problems.

  3. Alifanov, O. M., Inverse Heat Transfer Problems.

  4. Beck, J. V., Blackwell, B., and St. Clair, C. R., Inverse Heat Conduction: Ill-Posed Problems.

  5. Karkhin, V. A., Plochikhine, V. V., Ilyin, A. S., and Bergmann, H.W., Inverse Modelling of Fusion Welding Process.

  6. Lambrakos, S. G. and Michopoulos, J. G., Algorithms for Inverse Analysis of Heat Deposition Processes.

  7. Michopoulos, J. and Lambrakos, S., On the Fundamental Tautology of Validating Data-Driven Models and Simulations. DOI: 10.1007/11428848_95

  8. Michopoulos, J. G. and Lambrakos, S. G., Underling Issues Associated with Validation and Verification of Dynamic Data Driven Simulation. DOI: 10.1109/WSC.2006.322998

  9. Kirsch, A., An Introduction to the Mathematical Theory of Inverse Problems.

  10. Lambrakos, S. G. and Milewski, J. O., Analysis of Processes Involving Heat Deposition using Constrained Optimization. DOI: 10.1179/136217102225002646

  11. Xie, J. and Zou, J., Numerical Reconstruction of Heat Fluxes. DOI: 10.1137/030602551

  12. Hadamard, J., Sur les problèmes aux dérivées partielles et leur signification physique.

  13. Tikhonov, A. N. and Arsenin, V. Y., Solutions of Ill-Posed Problems.


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