FINITE ELEMENT SIMULATION OF WAVE MOTION ——Basic Problems and Conceptual Aspects
Liao Zhenpeng Liu Jingbo (Institute of Engineering Mechanics, SSB)
The artificial boundary condition is written in a compact form, which can be djrectly incorporated into finite elements. The discretization error and the oscillation instability are studied in detail for a simple one-dimensional model in order to clarify conceptual aspects of the two basic problems in the simulation. The discretization error is analyzed through studies on characteristics of wave motion in the discrete model and their differences from those in the corresponding continuum. The analysis leads to identifying a frequency band within which the simulation is possible,and to a suggestion of using the lumped-mass finite element model for the simulation. Mechanism of the oscillation instability is then illuminated in frequency domain by amplification at the artificial boundary and multi-reflection of wave motion in a finite discrete model. Understanding of the mechanism provides guidelines for seeking measures to guarantee the stable implementation of the artificial boundary, and a modification of the artificial boundary condition is then devised for eliminating the instability. The special stability criterion is finally presented for the modified boundary condition, in addition to the ordinary stability condition for the numerical integration of equation of motion at interior nodes.