透射边界零频飘移失稳数值解增长模式解释

Explanation for amplification mode of instable numerical solutions in multi-transmitting formula induced zero-frequency drift instability

高阶透射边界能高效吸收入射至人工边界波动,但其引发的一类典型的数值失稳问题-零频飘移失稳仍未得到很好解决。已有的零频飘移失稳机理还不完善,如难以解释数值模拟中观测到的飘移失稳现象。这一局部失稳现象表现为:失稳从人工边界节点开始,然后向计算区域内延拓;节点向一方向运动,而不再以其初始位置为中心振动。为此结合模态分析及Z变换,本文基于一维波动模型分析了飘移失稳机理及飘移失稳数值解增长模式与透射边界精度阶之间的关系。

Higher orders multi-transmitting formula （MTF） are superior in absorbing efficiency for outgoing waves impinged on artificial boundaries. However, one typical kind of MTF induced instability problems, that is zero-fre- quency drift instability, is still not well understood or being solved. The available mechanism of zero-frequency drift instability is far from perfect. It can not explain the observed drift instable phenomenon, starting from the artificial boundary nodes and extending later to interior nodes, inside which the motion of the node is not vibrating normally back and forth around the zero equilibrium point but move continuously along one side of the equilibrium point. Thus in this paper, based on a representative one-dimensional wave model, we give the mechanism of drift instability and furthermore we establish the relationship between the amplification mode of drifting numerical solutions with the accuracy order of MTF.