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

Bui Quoc Tinh,Nguyen Ngoc Minh,Nguyen Thanh Nha,Truong Tich Thien

doi:10.32508/stdj.v20ik9.1671

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.

Highlights

ONE may encounter heat transfer problems in many human activities
As alternatives to finite element (FEM), various other methods have been proposed for heat transfer analysis, such as the Boundary Element Method (BEM) [3] and the class of meshfree method [4, 5]
Proper Orthogonal Decomposition (POD) is combined with consecutive-interpolation finite element method (CFEM) to effectively save computational time in the context of three-dimensional transient thermal analysis, such that the applicability of CFEM is further expanded

Summary

INTRODUCTION

ONE may encounter heat transfer problems in many human activities. For example, all three types of heat transfer can be found in cooking, i.e conduction, convection and radiation. The standard finite element (FEM) [1] has been widely used for heat transfer problems due to its simplicity and reasonable accuracy. As alternatives to FEM, various other methods have been proposed for heat transfer analysis, such as the Boundary Element Method (BEM) [3] and the class of meshfree method [4, 5]. Investigation on combination of POD with finite element analysis of heat transfer problems is discussed by [11]. POD is combined with CFEM to effectively save computational time in the context of three-dimensional transient thermal analysis, such that the applicability of CFEM is further expanded.

Brief on consecutive-interpolation

Governing equations of heat transfer problems

Two-dimensional heat transfer

Three-dimensional heat transfer

Heat transfer in a 3D complicated domain

CONCLUSIONS