Applications of Discontinuous Galerkin Finite Element Method in Thermomechanical Coupling Problems with Imperfect Thermal Contact

Donghuan Liu,Yinghua Liu

doi:10.1155/2013/861417

Abstract

Thermomechanical coupling problems with imperfect thermal contact are analyzed in the present paper with discontinuous Galerkin finite element method. The imperfect thermal contact condition is characterized by thermal contact resistance. The whole thermomechanical coupling problem is solved alternatively with the thermal subproblem and mechanical subproblem. Thermal contact resistance is introduced directly with the interface numerical flux of the present discontinuous Galerkin finite element method without using interface element as traditional continuous Galerkin finite element method does. Numerical results show the accuracy and feasibility of the present discontinuous Galerkin finite element method in solving thermomechanical coupling problems with imperfect thermal contact.

Highlights

Thermomechanical coupling problems exist in many engineering fields, such as hypersonic aircraft structures, nuclear fuel elements, heat exchanger, and metal forming
Thermal contact resistance is caused by imperfect thermal contact; it arises in the contact region of two solids, as most of the heat through the interface flows through the actual contact spots, and this causes constrictions of heat flux lines through the bulk solid material of the contact interface, which leads to the thermal contact resistance
The main purpose of the present paper is to propose a scheme of the discontinuous Galerkin finite element method and demonstrate its application in the modeling of thermomechanical coupling problems caused by imperfect thermal contact

Summary

Introduction

Thermomechanical coupling problems exist in many engineering fields, such as hypersonic aircraft structures, nuclear fuel elements, heat exchanger, and metal forming. Liu et al presented a discontinuous Galerkin finite element method for the heat conduction problems with local high gradient and thermal contact resistance [18]. They proposed a discontinuous Galerkin finite element algorithm to solve the thermoelastic coupling problems caused by temperature and pressure dependent thermal contact resistance [19]. The main purpose of the present paper is to propose a scheme of the discontinuous Galerkin finite element method and demonstrate its application in the modeling of thermomechanical coupling problems caused by imperfect thermal contact. The methods presented by Zienkiewicz et al [20] and Zheng et al [19] for one-dimensional and two-dimensional problems are extended to three-dimensional situation

Formulation of the Discontinuous Galerkin Finite Element Method

Numerical Examples

Conclusions