Numerical simulation of shock wave focusing at fold caustics, with application to sonic boom

Weak shock wave focusing at fold caustics is described by the mixed type elliptic/hyperbolic nonlinear Tricomi equation. This paper presents a new and original numerical method for solving this equation, using a potential formulation and an "exact" numerical solver for handling nonlinearities. Validation tests demonstrate quantitatively the efficiency of the algorithm, which is able to handle complex waveforms as may come out from "optimized" aircraft designed to minimize sonic booms. It provides a real alternative to the approximate method of the hodograph transform. This motivated the application to evaluate the ground track focusing of sonic boom for an accelerating aircraft, by coupling CFD Euler simulations performed around the mock-up on an adaptated mesh grid, atmospheric propagation modeling, and the Tricomi algorithm. The chosen configuration is the European Eurosup mock-up. Convergence of the focused boom at the ground level as a function of the matching distance is investigated to demonstrate the efficiency of the numerical process. As a conclusion, it is indicated how the present work may pave the way towards a study on sonic superboom (focused boom) mitigation.