Residual Distribution Method for Aeroacoustics

Abstract

This article deals with the discretization of linearized Euler equations by multidimensional upwind residual distribution methods. Linearized Euler equations are applied to model the propagation of sound in the domain where no source of sound is present and where the analogy methods such as Ffowcs―Williams can not be used because of gradients in the mean flow. The residual distribution method leads to a class of schemes that shares properties of both finite element method and finite volume method. In particular, the schemes used here are multidimensional upwind, which make them very attractive because of their low cross-dissipation. First, the discretization method is introduced as an alternative method for computational aeroacoustic applications on unstructured grids. The residual distribution method is then analyzed analytically for wave propagation. Next it is applied to linearized Euler equations with proper acoustic boundary conditions, and finally verifiedon test cases having exact solution.