Multiscale Unsteady Conjugate Transfer via Modal Projection

This paper presents a multiscale methodology for efficient unsteady conjugate heat transfer simulations. The solid domain is modelled by coupling a global representation of the temperature field, based on the eigenfunctions of the unsteady heat conduction equation, with a local, fine-scale-resolving solution of the heat conduction equation at the conjugate interface. To address the disparate time scales and enhance convergence, the decoupled modal equations are leveraged to enable targeted acceleration of the longest thermal time scales. One-dimensional analyses validate the properties of the scheme, while scale-resolving simulations demonstrate its practical application for steady and unsteady problems. Notably, the method achieves up to a fourfold reduction in computational time to reach steady thermal conditions compared to conventional conjugate simulations, without introducing significant computational overhead or error, offering an accurate and accelerated framework for unsteady thermal analysis.