A fast reduced-order model for radial integral boundary element method based on proper orthogonal decomposition in nonlinear transient heat conduction problems

Abstract

In order to efficiently solve nonlinear transient heat conduction problem, a method combining the radial integration boundary element method (RIBEM) and the proper orthogonal decomposition (POD) is proposed to establish the nonlinear reduced-order model, and the implementation of the reduced-order model makes fast numerical simulation possible in engineering field. Transient heat conduction problems with temperature-dependent and temperature-independent thermal conductivity are firstly solved by the RIBEM respectively, and two types of snapshots are composed of these solved transient temperature fields. Subsequently, the POD is applied in the analysis of the snapshots, and then a set of optimal orthogonal basis can be obtained. In the procedure of establishing the reduced-order model, we need to redistribute the nonlinear equations. The strategy is to separate the boundary nodes defined as Dirichlet condition, and then the orthogonal basis is used to derive a reduced-order expression for the remaining unknowns. Therefore, the degree of freedom that needs to be solved can be greatly reduced. Numerical examples show that different reduced-order models based on nonlinear basis and linear basis are all consistent with the full-order model. What is more, the computational efficiency is greatly improved due to the introduction of the reduced-order model.