Numerical simulation of sonic boom focusing

A numerical method is presented to simulate the focusing of sonic booms. In the vicinity of caustics, the pressure satisfies the nonlinear Tricomi equation. To solve this equation, an iterative algorithm, based on an unsteady version of the equation, is used. The algorithm is a modification of the pseudospectral code used for solving the Zabolotskaya-Khokhlov (KZ) equation. In the linear case, the code is validated by comparison with analytical solutions. For an incoming N wave, the shape of the outgoing wave observed in flight tests is recovered. In the nonlinear case, no analytical solution is known to compare with the numerical output, Validation of the numerical scheme is completed by means of four different tests. First, comparisons with the linear case shows that the numerical solutions behave as expected from the physics. Second, the solution after convergence is proved to be independent of the initial guess. Third, the maximal signal amplitude is proved to converge while increasing the discretization. Finally, the numerical scheme is checked against the nonlinear Guiraud's scaling law. In the last part, an application to the focusing of Concorde sonic boom in acceleration is presented, and ways of reducing focused booms are discussed.