基于移动网格方法的移动热源热方程的数值模拟  

Numerical Simulation of Heat Equation of Moving Heat Source Based on Moving Mesh Method

作　　者：刘支会 LIU Zhi-hui(College of Science, Nanjing University of Aeronautics And Astronautics. Nanjing 210016, China)

机构地区：[1]南京航空航天大学理学院数学系,南京210016

出　　处：《西安文理学院学报（自然科学版）》2021年第1期1-7,共7页Journal of Xi’an University(Natural Science Edition)

摘　　要：致力于数值求解二维带δ函数奇异源的热方程.由于热源具有奇异性,如果能有一个网格点落在热源位置,就能实时跟踪热源的运动变化,为了达到这一目的,我们采用了区域分解.它还可以并行计算,提高计算效率.移动网格方法在网格点总数保持不变的前提下,通过调整网格点的位置使它集中于解变化较大的区域,从而获得比使用均匀网格时更高的精度.提出适合于该二维模型的基于区域分解的移动网格方法,并通过数值算例验证了算法的有效性.In this paper,we focus on the numerical solution of two-dimensional heat equation with singular source of function.Because of the singularity of the heat source,if a mesh point can be located at the heat source,the movement of the heat source can be tracked in real time.In order to achieve this goal,we use domain decomposition.It can also be used in parallel computing to improve computational efficiency.On the premise that the total number of mesh points remains unchanged,the moving mesh method can obtain higher accuracy than that of uniform mesh by adjusting the position of mesh points to make it concentrate on the region where the solution changes greatly.We propose a moving mesh method based on domain decomposition,and the numerical examples show the effectiveness of the algorithm.

关 键 词：移动网格方法 控制函数 移动热源 热方程 

分 类 号：O193[理学—数学]