Acoustic wave scattering from a circular crack: Comparison of different computational methods

The work reported was motivated by disagreement between the results obtained from two computations of scattering of an axially incident elastic p-wave on a circular crack. One calculation involves the direct solution of the Helmholtz integral equation, showing an oscillating total cross section. The other uses a program called MOOT, in which the elastic displacement near the crack is expanded in regular spherical eigenfunctions of the elastic wave equation. This calculation shows that the oscillations in total cross section disappear rapidly at high wave numbers. The conjecture that the basis for the MOOT expansion was inappropriate is examined by application to a test problem. Results indicate that there is no inadequacy in the spherical basis set.