Numerical Simulations of sonic booms in non-uniform flows

Sonic booms can be simulated based oil a small disturbance potential formulation which leads to a nonlinear mixed type equation similar to that of transonic flows [1]. Numerical results using Murman's scheme are given in [2] for 2-D and 3-D problems. In the present work, the governing equations axe written as a system of first-order equations in terms of the velocity components. The resulting system is a generalized form of Cauchy/Riemann equations with the vorticity as a forcing function. Using Crocco's relation, the vorticity call be related to the gradients of entropy and total enthalpy in general. for some applications, the entropy variation call be neglected and the isentropic flow model is adequate even with variable total enthalpy. The Cauchy-Riemann equations are solved numerically as in [4]. Artificial time dependent terms are introduced leading to a symmetric hyperbolic system, which is solved using standard numerical methods. Centered schemes are used with explicit artificial viscosity terms added to the equations for numerical stability. The artificial viscosity is constructed via a least squares procedure, as in [3], and additional dissipation is needed for shock capturing. Explicit time integration, which is fully parallelizable, is implemented to obtain steady state solution. Typical numerical results are shown for linear and parabolic velocity profiles of the main flow, with shock reflection ill the field and smooth signatures oil the ground.