Discussion On MTF Artifical Wave Velocity And Stability Coefficient Of Scattering Problem

The stability problem has always been a fundamental problem in multiple transmission boundaries,including high frequency oscillation instability and zero frequency drift instability.many scholars have conducted in-depth research on the stability of the transmission boundary,and gradually improved the theoretical basis and practical application of the transmission boundary,but there are still some problems;artificial wave velocity,as an empirical parameter of the transmission boundary,is rarely studied.In this paper,a finite element method is used to analyze the scattering of plane SV waves from uniform half-space model and concave terrain.The displacement responses of nodes and boundary nodes in the calculation area are analyzed when the first-order to fourth-order transmission boundary is incident vertically.The effects of artificial wave velocity,damping and drift elimination coefficient are also considered.The results are extended to higher-order cases.The main results are as follows:(1)The order N of the transmission boundary has the same effect on the numerical simulation results of the uniform half space and the depression terrain.The higher the order N of the transmission boundary is,the higher the accuracy of the numerical simulation results will be,but the earlier the high frequency oscillation occurs,and the more likely the drift instability will occur.(2)The results of numerical simulation of artificial wave velocity are different between uniform half-space and depression topography.In the range of 0-2 times of incident wave velocity,for uniform half-space,the artificial wave velocity takes priority of0.5 times of incident wave velocity;for depression topography,the artificial wave velocity takes priority of incident wave velocity.The earlier the artificial wave velocity is larger than the incident wave velocity,the earlier the high frequency instability occurs,the more intense the drift instability and the worse the accuracy.When the artificial wave velocity is smaller than the incident wave velocity,the higher the accuracy of numerical simulation is for the uniform half-space model,and the lower the accuracy of numerical simulation is for the depression topography.(3)Damping can effectively delay the occurrence of high frequency instability,and the effect of damping on the numerical simulation results of uniform half space and depression terrain is consistent.The greater the damping is,the later the high frequency instability occurs.The larger the order N of the transmission boundary is,the greater thedamp is needed to eliminate the high-frequency instability.For the uniform half-space and the depression terrain,the damp needed to eliminate the high-frequency oscillation of the numerical simulation results of the depression terrain is larger than that of the uniform half-space.(4)The addition of drift elimination coefficient can effectively solve the drift instability,but the effect of drift elimination coefficient depends on the value of r operator.For uniform half-space and depression terrain,the drift coefficient needed to eliminate the drift instability of numerical simulation results of depression terrain is larger than that of uniform half-space.The larger the order N of transmission boundary,the larger the R value needed to eliminate drift instability.A slightly larger drift removal coefficient will not have a significant impact on the numerical simulation results of uniform half-space,but will cause a reduction in the accuracy of the numerical simulation results of depression topography.