Reduced Order Modeling for Spatially Varying Radiative Interfaces

Abstract

Radiative heat transfer between moving geometries is critical in many high-temperature engineering systems, yet existing simulation approaches are often too computationally expensive. This study addresses this challenge by developing and testing a reduced order modeling framework for a transient, coupled, nonlinear radiative heat transfer problem with spatially varying subsystems.

We implemented a finite element model of two geometries in Python as a test problem, incorporating the nonlinear radiation boundaries, and varying view factors due to the motion between the subsystems. Different model order reduction techniques are applied on the test problem, each facing distinct limitations. The spatially varying nonlinearity caused most of the complexities. This nonlinearity is solely on the boundary, hence we use substructuring to isolate the nonlinearity. The linear internal dynamics can be reduced with well-established reduction techniques, like the Craig-Bampton method. In addition, the nonlinear boundary term is approximated by a feedforward neural network that was trained on simulation data to approximate nonlinear radiation exchange as a function of the temperatures on the radiative boundaries and relative position, enabling us to ignore the view factor computations, which are computationally very expensive.

The proposed reduced order model (ROM), combining Craig-Bampton reduction for internal degrees of freedom with a neural network approximation for interface radiation, achieves significant computational savings compared to the full order model (FOM).
Results show that with decoupling internal and interface dynamics, the Craig-Bampton basis reduces the system matrices sizes while preserving accuracy in the full solution.
On the interface, the neural network provides an efficient approximation for the nonlinear, spatially varying radiation operator, reducing the computational costs from quadraticn, O(NM), scaling (FOM) to a linear, O(N+M), dependence, where N and M are the number of elements on the radiative boundaries of two components.
In time integration, the Newton iterations remain identical in terms of the setup to the full model, but the reduced residual and Jacobian evaluations are significantly faster as the matrix sizes are reduced.
Although both the Craig-Bampton reduction and neural network require additional offline computations (modal analysis and training), these are one-time costs.
The online benefits are significant: the ROM reproduces the full solution very accurately while enabling much faster simulations, making it very useful for repeated evaluations, parametric-, and design studies.