Domain Decomposition Methodology with Robin Interface Matching Conditions for Solving Strongly Coupled Fluid-Structure Problems

Abstract

The inverse energy deposition problem represents a particular subclass of the more general inverse heat conduction problem, where certain features that are associated with upstreamto- 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.