【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.更多还原

【Abstract】 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.更多还原