Numerical Investigation of Heat Conduction with Multiple Moving Heat Sources

Zhicheng Hu

doi:10.3390/sym10120673

Abstract

This paper is concerned about the efficiently numerical simulation of heat conduction problems with multiple heat sources that are allowed to move with different speeds. Based on the dynamical domain decomposition upon the trajectories of moving sources, which are solved by a predictor–corrector algorithm, a non-overlapping domain-decomposed moving mesh method is developed. Such a method can not only generate the adaptive mesh efficiently by parallel computing, but also greatly simplify the discretization of the underlying equations without loss of accuracy. Numerical examples for various motions of sources are presented to illustrate the accuracy, the convergence rate and the efficiency of the proposed method. The dependence of the solution on the moving sources such as the types of motion and the distance between sources is numerically investigated. A blow-up phenomenon that occurs at multiple locations simultaneously can also be well observed for the case of symmetrically moving sources.

Highlights

The heat conduction transfer of problems with moving heat sources has attracted a great deal of interest by engineers in the past few decades
Typical applications include contact surfaces such as free-boundary solidification [1], and many metallurgical processes such as laser cutting and welding [2,3,4,5]. This problem can be well modeled by the heat conduction equation with singular source terms, which utilize a time-dependent delta function to describe each highly localized and moving heat source
Motivated by the above observation, this paper focuses on the development of the moving mesh method for problems with multiple moving heat sources, whose motions are controlled by different ordinary differential equations

Summary

Introduction

The heat conduction transfer of problems with moving heat sources has attracted a great deal of interest by engineers in the past few decades. Typical applications include contact surfaces such as free-boundary solidification [1], and many metallurgical processes such as laser cutting and welding [2,3,4,5]. This problem can be well modeled by the heat conduction equation with singular source terms, which utilize a time-dependent delta function to describe each highly localized and moving heat source (see [1,3,6,7] and references therein). Numerical simulation to investigate the solution phenomenon, such as the prediction of the blow-up time, accurately and efficiently still remains big challenges

Objectives

Methods

Conclusion