NUMERICAL-SOLUTION OF THE KZK EQUATION FOR FOCUSING SOURCES

Numerical methods for solving the KZK equation with the equivalent bou ndary condition, which is used in the description of focusing sound so urces, are studied. For focusing sources the Transformed Beam Equation (TEE) is an interesting alternative to the KZK equation because it al lows the application of focusing numerical grids. For large gains a co mbination of the ordinary KZK equation and the TEE, performs well. In the case of smaller gains the best results are obtained solving equati ons corresponding to the ordinary KZK equation. At the open boundaries a flow relaxation scheme is applied, and reflections of outgoing wave s into the computational domain are avoided.