Efficient numerical analysis of transient heat transfer by Consecutive-Interpolation and Proper Orthogonal Decomposition

Abstract

The consecutive-interpolation technique has been introduced as a tool enhanced into traditional finite element procedure to provide higher accurate solution. Furthermore, the gradient fields obtained by the proposed approach, namely consecutive-interpolation finite element method (CFEM), are smooth, instead of being discontinuous across nodes as in FEM. In this paper, the technique is applied to analyze transient heat transfer problems. In order increase time efficiency, a model- reduction technique, namely the proper orthogonal decomposition (POD), is employed. The idea is that a given large-size problem is projected into a small-size one which can be solved faster but still maintain the required accuracy. The optimal POD basis for projection is determined by mathematical operations. With the combination of the two novel techniques, i.e. consecutive-interpolation and proper orthogonal decomposition, the advantages of numerical solution obtained by CFEM are expected to be maintained, while computational time can be significantly saved.

Estimation of heat transfer parameters by using trained POD-RBF and Grey Wolf Optimizer

“…In this work, nodal values of temperature at all nodes obtained by direct solution of finite element analysis are taken as the training data. Following the terminology used in literatures [21][22][23][24]30], each column of training data is called a snapshot, and the matrix of training data itself is called the snapshot matrix…”

“…The process is time-consuming and needs to be accelerated. The model order reduction technique Proper Orthogonal Decomposition (POD) has been successfully employed in direct heat transfer problems [21][22][23][24]. The core idea is to find a set of orthogonal vectors (POD bases) using singular value decomposition, which is then utilized to approximate the temperature field.…”