Prediction of Superboom Problem Using Computational Solution of Nonlinear Tricomi Equation

Abstract

The sonic -boom focusing problem has been solved using the nonlinear Tricomi equation. A pseudo time term has been added to the equation so that marching in pseudo time will be possible. The solution to this equation is obtained by splitting the nonlinear equation into two parts: a part corresponding to a linear unsteady Tricomi equation, and another part as the nonlinear unsteady Burgers equation. The solution of the unsteady li near Tricomi equation is followed by the solution of the nonlinear unsteady Burgers equation to obtain the solution of the total nonlinear equation. Three computational schemes are used. The first is a frequency -domain (FD) fast –Fourier transform (FFT) sch eme, the second is a time domain (TD) finite -difference scheme, and the third is a TD finite -difference scheme with overlapping grid (OLG). Numerical examples include an N -shape wave, a Concorde aircraft wave, and other flat -top and ramp -top waves. Superb oom of these signals at caustic surfaces has been predicted successfully, and the results of the different schemes have been compared. The equation has also been solved in the conservative form without any splitting. The computational scheme is a TD type differencing scheme. The results have been compared with the other three computational schemes. The CTD scheme is much more efficient than the others.