Numerical Simulation Of Heat Conduction In A 2D Moving Heat Source Problem

This paper is devoted to numerically simulating the heat conduction phenomenon of two-dimensional moving heat source.The heat conduction problem of moving heat source is widely used in laser cutting,welding,cladding,laser heat treatment and other industrial processes.Many scholars are devoted to the study of temperature changes caused by the movement of heat sources in physical regions.The moving heat source problem has usually singularity,and the moving mesh method can solve it efficiently.As one of the adaptive mesh methods,the moving mesh method has attracted more and more attention in recent decades and it has been widely used in the fields of computational fluid dynamics,multiphase flow,crystal growth,reaction diffusion,biological calculation and other fields.We take the heat equation with moving Gaussian heat sources as an example to study the application of the moving mesh method in moving heat source problems,and propose a simple and effective moving mesh method.On the basis of the one-dimensional moving mesh method,this method continuously adjusts the two-dimensional mesh dimension by dimension,that is,solving the one-dimensional moving mesh in the x direction and the y direction respectively,constructing the two-dimensional mesh with the two groups of one-dimensional meshes.Based on the rectangular mesh,the finite difference numerical model with second order accuracy is established using Crank-Nicolson scheme for the physical equation under moving mesh.Numerical experiments show that the proposed moving mesh algorithm can effectively and accurately simulate the problem of moving heat sources and the transient heat conduction phenomenon caused by various parameters of the moving heat source,such as the number of heat sources and the type of motion.Compared to the uniform mesh method,the moving mesh method can obtain higher accuracy by adjusting the position of the mesh points so that it focuses on the place where the solution changes relatively large.The full text is divided into four chapters.Chapter 1 introduces the research background and current situation of the moving mesh method and the moving heat source problems,as well as the content arrangement of this paper.Chapter 2 mainly introduces the knowledge of moving mesh method,in which the principle of equidistribution is introduced in detail.Based on the principle of equidistribution,we introduce the relevant knowledge of the moving mesh partial differential equations and monitor functions.Chapter 3 mainly introduces the numerical research of the moving heat source problem using the moving mesh method.We simulates some numerical examples,including the case of linear motion,circular motion and sinusoidal motion of a heat source,and linear motion of multiple heat sources.There are many ways to select the monitor function,we often select arc length monitor function or curvature monitor function for calculations.If the monitor function is selected differently,the effect of mesh movement will be different,so we discuss the effect of different monitor functions on the numerical solution.Chapter 4 gives brief summary and future work of the problem studied.