Investigating the performance of model order reduction techniques for nonlinear radiative heat transfer problems

The problem of nonlinear radiative heat transfer is one of great importance to the aerospace industry.
However, analysing large-scale, nonlinear, multiphysical, dynamical structures, by using mathematical
modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally expensive. This provides motivation for the development of Model-Order Reduction (MOR) techniques capable of reducing simulation times without the loss of important information. The objective is to demonstrate the method of Proper Orthogonal Decompostition (POD) as a technique for nonlinear MOR. The nonlinear radiative exchanges between a linear benchmark beam within an external box (Figure 1) are analysed and a reduction procedure for this fully coupled, nonlinear, multiphysical,
thermomechanical system is established. The solution to the strongly coupled, thermomechanical equations of motion is found by making use of an extended version of the implicit generalized-alpha scheme. In the reduced model, the residual of the unreduced system of equations need to be evaluated at each Newton iteration of each time step. In order to optimise the efficiency of the reduction method it is shown that the internal forces can be split into their linear and nonlinear counterparts. Only the nonlinear terms change at each time step, thus only these terms need to remain in the iterative loop significantly reducing the number of parameters that are to be computed at each step. These efficiency improvements to the method are discussed and the results are given.