Application of the CABARET and WENO Schemes for Solving the Nonlinear Transport Equation in the Problem of Simulating the Propagation of a Sonic Boom Wave in the Atmosphere

The most convenient model describing the propagation of a sonic boom wave in the atmosphere is the augmented Burgers equation. In this work, we studied the influence of a numerical scheme on the result of solving an equation that takes into account the nonlinear nature of the propagation of sonic boom waves in the atmosphere. This equation is a key component of the augmented Burgers equation and determines the nature of the transformation of the disturbed pressure profile during its propagation. Two numerical schemes were used for solving: CABARET and WENO—quasi-monotonic end-to-end computing schemes, which make it possible to obtain a solution without significant numerical oscillations. The applicability of these schemes for solving the problem under consideration is analyzed.