Acoustic analogy methods are used as post-processing tools to predict aerodynamically generated sound from numerical solutions of unsteady flow. The Ffowcs WilliamsHawkings (FW-H) equation and related formulations, such as Farassat's Formulations 1 and 1A, are among the commonly used analogies because of their relative low computation cost and their robustness. These formulations assume the propagation of sound waves in a medium at rest. The present paper describes a surface integral formulation based on the convective wave equation, which takes into account the presence of a mean flow. The formulation was derived to be easy to implement as a numerical postprocessing tool for computational fluid dynamics codes. The new formulation constitutes one possible extension of Farassat's Formulation 1 and 1A based on the convective form of the FW-H equation.

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A fourth-order, implicit, low-dispersion, and low-dissipation Runge-Kutta scheme is introduced. The scheme is optimized for minimal dissipation and dispersion errors. High order accuracy is achieved with fewer stages than standard explicit Runge-Kutta schemes. The scheme is designed to be As table for highly stiff problems. Possible applications include wall-bounded flows with solid boundaries in the computational domain, and sound generation by reacting flows.