Numerical validation of a computer code developed to study sonic boom focusing modeled by the Khokhlov-Zabolotskaya-Kuznetsovequation

摘要

This paper describes a numerical validation of computer code that implements anaugmented version of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) model equation. Themain purpose for this code is to examine the effects of sonic boom focusing in the regionsurrounding a caustic cusp. The model equation is solved using a splitting method andincludes terms for diffraction, nonlinearity, absorption and dispersion. There are severalapproaches in the literature for numerical validation of the nonlinearity andabsorption/dispersion mechanisms. However, the approach for the numerical validation ofthe diffraction term was chosen based on the particular application for the computer code,which in this case, is the study of focusing effects of sonic booms. The prototype problemexamined was the pressure field in the vicinity of a caustic cusp due to cylindrical wavefocusing in two dimensions. The resulting analytical solution includes the Pearcey integraland is the basis for the numerical validation of the diffraction term. The code in thepresent paper benchmarked very well for all components of the KZK model equation,including the diffraction term.