A dispersion-relation preserving fourth-order compact time-domain/frequency-domain finite-volume method for computational acoustics

A method for directly computing acoustic signatures without a wave equation analogy is presented. The governing acoustic equations are derived from the unsteady Euler equations by linearizing about a steady mean flow and by assuming a single frequency disturbance. A pseudo-time variable is introduced, and the entire set of equations is driven to convergence by a point implicit four-stage Runge-Kutta timemarching finite-volume scheme. The spatial terms are discretized using a compact fourth-order accurate dispersion-relation-preserving scheme. A compact sixth-order-accurate dissipation operator is introduced to damp out physically nonrealizable spurious modes which are the artifact of numerical discretizaton. A new formulation of the farfield causality condition is presented which is based on the modal analysis of the similarity form of the linearized Euler equations. The method has been applied to compute acoustic radiation from compact and non-compact oscillating airfoils in the presence of mean flow, acoustic radiation due to airfoil/gust interactions, acoustic scattering from airfoils, and wave propagation in ducts. Results are compared with known analytical solutions and the results of other investigators where applicable.