Numerical solution of acoustic propagation problems using linearized Euler's equations

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Some numerical solutions of acoustic propagation problems using linearized Euler equations are studied. The two-dimensional Euler equations are linearized around a known stationary mean flow. The computed solution is obtained by using a dispersion-relation-preserving scheme in space, combined with a fourth-order Runge-Kutta algorithm in time. This numerical integration leads to very good results in terms of accuracy, stability, and low storage. The implementation of source terms in these equations is studied very carefully in various configurations, inasmuch as the final goal is to improve and to validate the stochastic noise generation and radiation model. In this approach, the turbulent velocity field is modeled by a sum of random Fourier modes through a source term in the linearized Euler equations to predict the noise from subsonic flows. The radiation of a point source in a subsonic and a supersonic uniform mean flow is investigated. The numerical estimates are shown to be in excellent agreement with the analytical solutions. Then, the emphasis is on the ability of the method to describe correctly the multipolar structure of aeroacoustic sources. The radiation of dipolar and quadrupolar extended sources is, thus, studied. Next, a typical problem in jet noise is considered with the propagation of acoustic waves in a sheared mean flow. The numerical solution compares favorably with ray tracing. Finally, a nonlinear formulation of Euler's equations is solved to limit the growth of instability waves excited by the acoustic source terms.