A Highly Efficient Semi-Implicit Two-Field Modeling for Thermal Contact Problems with Non-Fourier Effects

In this paper, we revisit the thermal interface condition of thermal contact problems with a nonzero thermal resistance. We point out that continuity conditions of the flux at the interfaces, which usually adopt the form of temperature gradient in numerical simulations of thermal contact problems, leads to a paradoxical result if one of the adjacent bodies has zero temperature gradient. Specifically, that using the temperature gradient instead of the real heat flux yields a nonphysical temperature profile and fails to depict the thermal jump in cases with zero temperature gradients. We then show that by using a two-field (temperature and flux) formalism, in lieu of the classical single-field (temperature) naturally resolves this paradox. Given that the fully implicit scheme requires an extremely large solve in the two-field model, we propose an easy-to-implement semi-implicit scheme for this two-field formulation. The proposed semi-implicit computational framework for thermal interface problems is formulated in the fashion of differential algebraic equations (DAEs), in which the interface conditions are treated as algebraic equations constraining the associated heat process governed by differential equations. Our method can precisely fulfill the interface condition with the magnitude of machine error (10-16) and is computationally more efficient (around 8 to 10 [[EQUATION]] faster) since it only needs to solve a very small Poisson-like system. Moreover, our method allows to investigate the thermal contact between either Fourier- and/or nonFourier- types with zero/nonzero thermal resistances by leveraging the generalized Jeffreys'-type heat flux model to describe the individual heat process in different adjacent domains. We present end-to-end 1D and 2D simulations of thermal contact problems to demonstrate the versatility and efficacy of our new method