Highly stable RK time advancing schemes for Computational Aero Acoustics

In this paper a brief survey of finite difference methods and time discretization schemes for the numerical simulation of problems in Computational Aero Acoustics (CAA), with special emphasis in the contributions of the authors in the last years to the subject, is presented. Due to the specific properties of these problems it is shown by means of some illustrative examples that standard schemes have some drawbacks and new numerical schemes have been derived taking into account not only the usual stability and accuracy requirements but also the dissipation and dispersion properties as well as low storage requirements. Some relevant contributions to the subject are presented comparing the relative merits by means of a Fourier analysis and numerical experiments. © 2010, Sociedad Española de Matemática Aplicada.