Discussion On MTF Stability Coefficient Of Wave Source Problem

In this paper,the implicit lumped mass finite element method and the local transmission artificial boundary are used to simulate the wave source problem in the near-field wave propagation.The transmission formulas are developed from the firstorder and second-order transmission boundary to the third-order and fourth-order transmission boundary by using two different modes of action: concentrated load and uniform load.The instability phenomena in the numerical simulation process are given.The effects of different viscous damping ratios on eliminating high frequency instability are quantitatively analyzed,and the effects of adding anti-drift instability coefficients on the drift instability of high order transmission boundary numerical solutions are discussed.The following conclusions are drawn:(1)When only high-frequency filtering measures are applied,in a certain time range,small viscous damping is added to eliminate the high-frequency oscillation in the numerical solution of low-order transmission boundary.When the viscous damping continues to increase to about one-thousandth of a million,the high-frequency oscillation in the numerical solution of high-order transmission boundary can also be completely eliminated;after high-frequency filtering,the numerical solution is applied to suppress drift instability.When the coefficient value is one thousandth,the drift instability of the numerical solution of the low-order transmission boundary can be eliminated basically,and the drift instability of the numerical solution of the high-order transmission boundary can also be eliminated.(2)Comparing the displacement time histograms under concentrated load and uniform load,it is found that the time of drift instability of uniform load is earlier than that under concentrated load,and the time of high frequency instability of numerical solution under concentrated load is earlier than that under uniform load.When the boundary size of the model is fixed,and in a certain time range,when N increases,the earlier the drift instability occurs and the greater the strength of the instability occurs in the MTF numerical solution;when N increases,the larger the parameter coefficients needed to suppress the instability(high frequency instability and drift instability)in the MTF numerical solution are;and when N increases,the higher the accuracy of the MTF numerical solution is.