摘要
将一维波动时域数值模拟的一种显式方法推广到二维,导出了二维非规则网格的节点递推公式.针对均匀正方形网格详细论述了时空精度皆为2M阶(M为正整数)的稳定递推公式的构建方法,并以构建二阶(M=1)和四阶(M=2)公式为例予以说明.最后,通过算例检验了本文研究结果,特别是说明了高阶公式对提高计算效率的价值.
For numerical simulation of wave motion,this paper generalizes the explicit method for 1-D wave equation to 2-D case,and develops the corresponding recursion formulas for an irregular grid for 2-D wave equations.For uniform quadrate grids,an approach to construct 2M-order stable formulas is discussed in detail,with M being a positive integer,which is illustrated by constructing second-order（M = 1） and fourth-order （M = 2） formulas.By numerical tests,the theoretical results presented in the paper are demonstrated, in which the effect of highly accurate recursion formulas in improving calculation efficiency is emphasized.
出处
《力学学报》
EI
CSCD
北大核心
2010年第6期1104-1116,共13页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家重点基础研究发展计划(973计划)(2007CB714200)
国家自然科学基金重大研究计划(90715038)资助项目~~
关键词
二维波动方程
数值模拟
显式递推公式
有限元
2-D wave equation numerical simulation explicit recursion formula finite element method（FEM）
