Abstract
Fast and accurate reduced order models (ROMs) of conductive-radiative systems are important for several industrial applications such as spacecraft, radiant furnaces, solar collectors, etc. The non-linear nature of radiative heat transfer limits the accuracy of the traditional proper orthogonal decomposition (POD) based approach, which works best in the linear realm. Optimal projection schemes based on least-squares minimization of time discrete residual, have shown great promise for solving non-linear convection-diffusion problems. The accuracy and efficiency of the approach relies on the critical assumptions relating to the low dimensional structure of the residuals, Jacobians and a reduced sample mesh, required for hyper-reduction. We argue that these assumptions may not hold true for the problems involving radiation. We investigate a coupled conduction and enclosure radiation problem to establish this claim. First, we demonstrate that LSPG-ROM indeed gives higher accuracy than POD-ROM for the same reduced dimension. Further, we show that, while hyper-reduction can be used to obtain significant computational gain for the residual approximation, this is not the case for the Jacobian approximation, as Jacobian snapshots exhibit a very slow singular value decay. Moreover, we find that the sample mesh size is in-fact close to the full order model (FOM) dimension, hence making the computational cost dependent on FOM dimension. Finally, we reinforce above observations by performing an exhaustive performance analysis to compare and characterize the computational cost of FOM, LSPG and hyper-reduced LSPG-ROMs.
