NUMERICAL-SOLUTION OF THE KZK EQUATION FOR FOCUSING SOURCES

Numerical methods for solving the KZK equation with the equivalent boundary condition, which is used in the description of focusing sound sources, are studied. For focusing sources the Transformed Beam Equation (TEE) is an interesting alternative to the KZK equation because it allows the application of focusing numerical grids. For large gains a combination of the ordinary KZK equation and the TEE, performs well. In the case of smaller gains the best results are obtained solving equations corresponding to the ordinary KZK equation. At the open boundaries a flow relaxation scheme is applied, and reflections of outgoing waves into the computational domain are avoided.