Computational Solution of Nonlinear Tricomi Equation for Sonic Boom Focusing and Applications

摘要

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 is obtained by splitting the nonlinear unsteady equation into two parts: a part corresponding to a linear unsteady Tricomi equation, and another part corresponding to an unsteady nonlinear Burgers equation. The solution of the linear unsteady Tricomi equation is followed by the solution of the nonlinear unsteady Burgers equation to obtain the solution of the total nonlinear equation. The solution of the linear unsteady Tricomi equation has been accomplished using two schemes. The first is a frequency-domain (FD) spectral scheme and the second is a time-domain (TD) finite-differencing scheme. The solution of the nonlinear unsteady Burgers equation has also been accomplished using two schemes. The first is a finite-difference scheme and the second is an analytical scheme. Thus, there are four combinations to obtain the solution of the nonlinear Tricomi equation.