变形法移动网格求解双曲型守恒律方程研究  

Research of Moving Mesh Method Based on Deformation in Solving Hyperbolic Conservation Laws

作　　者：陈冬冬[1,2] 宋松和[1] 

机构地区：[1]国防科学技术大学理学院 [2]中国人民解放军63892部队

出　　处：《计算机技术与发展》2010年第2期1-4,8,共5页Computer Technology and Development

基　　金：国家自然科学基金资助项目(10571178)

摘　　要：在现有格式的基础上要提高偏微分方程数值解的分辨率,自适应移动网格技术是一种有效而且可行的方法。文中将文献[1]提出的自适应移动网格技术推广到三角形网格,并将该方法用于求解双曲型守恒量方程。用网格自适应技术求解守恒律问题时,当生成新网格之后,需要将旧网格上的函数值更新到新的网格,并保持物理量的守恒性。针对这个问题,文中提出了函数值更新过程中守恒型插值公式的具体形式,并针对二维双曲型守恒律方程进行了仿真实验,取得了满意的结果。The adaptive moving mesh method is an efficient and practicable method to enhance the resolution of numerical solution of partial differential equation. Based on the scheme,this paper develops the moving mesh method based on deformation which Liao presented in reference [ 1 ] to triangular meshes. When applying adaptive mesh method in solving conservative laws, conservative variables must be updated on new mesh. Conserdering about this condition,the paper gives the updated equation from old mesh to new mesh in accurate form, and then apply the method to 2 - D hyperbolic conservation laws. The simulation experiment results denot that this method is efficient.

关 键 词：变形法 移动网格 双曲型守恒律方程组 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]