Simplification of Numerical and Analytical Tools for Sonic Boom Description

Numerical and analytical tools for aircraft sonic boom description are discussed in the light of the state of the art and development trends in methods for mathematical simulation of sonic booms. It is noted that an increasing role is played by numerical methods with mesh adaptation as applied to the steady Euler equations (in an aircraft-fixed frame in cruising flight) at distances from several to two ten body lengths. Another important tendency is that the complicated numerical–analytical approach to the mid- and far-field sonic boom description developed from the mid-20th century has been replaced by simpler approaches, including ones without using the Whitham function. As a development of these tendencies, we demonstrate that wave structures typical of sonic booms can be numerically computed using the Euler equations without constraints on distances and on the shock wave intensities, including extremely small ones. The description of the sonic boom evolution at distances of 15–20 body lengths to the ground is reduced to nearly immediate solution of Cauchy problems for ordinary differential equations that are consequences of the axisymmetric Euler equations. The viscous smearing of weak shock waves is described by the well-known one-dimensional stationary solution of the Navier–Stokes equations.