Investigation of fast GPU-based algorithms for jet-surface interaction noise calculations

The canonical problem of a jet flow interacting with a plate positioned parallel to the level curves of the streamwise mean flow has received much attention in Aero-acoustics research com- munity as a representation of jet installation effects. Rapid-distortion theory (RDT) modeling of this scenario involves relating an upstream convected quantity that serves as the problem in- put to measureable turbulence and then determine the far field radiated sound, as the response to this. The latter is found by solving the resulting Wiener-Hopf problem on a discontinuous surface subject to a gust-induced boundary condition across the vortex sheet shed of the trail- ing edge. Goldstein, Leib & Afsar (J. Fluid Mech., Vol. 881, pp. 551-584, 2019) find that the acoustic spectrum for the round jet scattering problem is given a formula that involves the computation of 4 integrals. Two of these are required to be computed at each point of the two-dimensional domain at a given frequency. Additionally, nested within these integrals is a Fourier transform of the turbulence correlation R22. In GLA19 this Fourier transform was found analytically however for different approximations of R22 this isn’t possible and it needs to be found numerically. Computation of this form of the solution is naturally computationally expensive on standard desktop computers. In this paper we therefore devise and investigate various algorithms in which the integrals are solved numerically on a GPU card. In gen- eral our calculations using the GPU algorithm show considerable reduction in computational time thus making this approach a viable option for design/optimization calculations aimed at characterizing the acoustic signature.