Model reduction in linear heat conduction: use of interface fluxes for the numerical coupling

Abstract In the framework of numerical modelling in transient heat conduction, it is shown in this paper, how to introduce different kinds of coupling on a part of the domain boundary without changing the original matrices of the model. The technique uses specific fluxes applied to the boundary which is treated: at each time step the coupling variables—temperatures and fluxes—are computed at first, and then, the influence of the fluxes are distributed on the rest of the domain and no iteration procedure is used. This permits the treatment of unexpected problems such as: variations of heat transfer coefficients, model connection and radiative boundary conditions. The method is particularly well adapted to a reduced model which acts as a substitute for a detailed model with diminution of computation time. Although the reduced model is obtained with some kind of boundary conditions and usually functions within the latter, with these coupling fluxes, the reduced model can also be used in other conditions.

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