On highly convergent 2D acoustic and elastic wave propagation models

摘要

The presented approach for reducing the phase and group errors in short wavelength pulses propagation modelling is based upon modal error minimization. A computational model is built of component substructures (CS) the matrices of which are obtained by modal synthesis. The necessary modal properties of CS are established by solving the cumulative modal error minimization problem for a sample domain the exact modal frequencies of which are known theoretically. Earlier the approach has been demonstrated to work well in 1D case. In this work the results for 2D rectangular meshes describing elastic and/or acoustic wave propagation have been obtained. As a result, models having up to 80% of modal frequencies with an error less than 2% can be obtained by using the optimized component substructures. Though the synthesized mass matrices are non-diagonal, the obtained dynamic models are able to simulate short transient waves and wave pulses propagating in elastic or acoustic environments by using only a few nodal points per pulse length.