Load Snapshot Decomposition to Consider Heat Radiation in Thermal Model Order Reduction

Abstract

Heat exchange by radiation in thermal field problems which corresponds to the fourth power of the temperature leads to nonlinear system equations. Hence, simulation times increase drastically, especially when parameter studies or sensitivity analyses are performed. Model order reduction is used to overcome these difficulties by projecting the model into a subspace of much smaller dimension. Heat radiation is treated as a part of the load vector resulting in constant system matrices. However, thermal loads like convection and radiation are distributed over the whole surface. That is why a high percentage of the nodes within the finite element model serves as inputs and outputs of the system. Thus, the Krylov subspace method cannot be applied directly as the reduced dimension depends on the number of inputs and would be too large.Therefore, input reduction becomes necessary and loads changing synchronously are clustered into one input. Furthermore, in the approach presented here load vector snapshots are taken from a training simulation of a reference configuration. The input matrix determination bases on the singular value decomposition of the snapshot matrix. Using only the singular vectors corresponding to the highest singular values reduces the number of inputs by several orders of magnitude allowing the application of model order reduction. Parameter variations can be performed yielding good results within a broad parameter range. The computational effort for the derivation of the snapshots is significantly decreased in comparison to conventional methods.