The paper addresses the construction of a non spurious mixed spectral finite element (FE) method to problems in the field of computational aeroacoustics. Based on a computational scheme for the conservation equations of linear acoustics, the extension towards convected wave propagation is investigated. In aeroacoustic applications, the mean flow effects can have a significant impact on the generated sound field even for smaller Mach numbers. For those convective terms, the initial spectral FE discretization leads to non-physical, spurious solutions. Therefore, a regularization procedure is proposed and qualitatively investigated by means of discrete eigenvalues analysis of the discrete operator in space. A study of convergence and an application of the proposed scheme to simulate the flow induced sound generation in the process of human phonation underlines stability and validity.

This paper discusses analytical and numerical issues related toelliptic equations with random coefficients which are generallynonlinear functions of white noise. Singularity issues are avoidedby using the Itô-Skorohod calculus to interpret the interactionsbetween the coefficients and the solution. The solution is constructedby means of the Wiener Chaos (Cameron-Martin) expansions. Theexistence and uniqueness of the solutions are established underrather weak assumptions, the main of which requires only that theexpectation of the highest order (differential) operator is anon-degenerate elliptic operator. The deterministic coefficientsof the Wiener Chaos expansion of the solution solve a lower-triangularsystem of linear elliptic equations (the propagator). This structureof the propagator insures linear complexity of the related numericalalgorithms. Using the lower triangular structure and linearity of thepropagator, the rate of convergence is derived for a spectral/hp finiteelement approximation. The results of related numerical experiments arepresented.