Development of a high-order compact algorithm for aeroacoustics employing PML absorbing boundaries

A finite-difference method for solving the twodimensional linearized Euler equations in terms of the acoustic variables is described. The far-field boundary conditions are approximated by the perfectly-matched-layer (PML) equations, which simulate an absorbing layer surrounding the interior of the computational domain. The spatial derivatives are represented by high-order compact differences, while the four-stage Runge-Kutta method is used to integrate the equations forward in time. Several benchmark problems have been computed with this technique, including propagation of a linear wave, and convection of acoustic and vortical disturbances in a uniform flow. The results obtained with fourth-order, sixth-order and eighth-order compact difference methods are presented. The compact method gives high resolution on a relatively small difference stencil. Progression from the fourth-order to the sixth-order and eighth-order schemes is straightforward. The PML approximation worked well in suppressing nonphysical reflections at the boundaries of the domain. The boundary error can be controlled or eliminated by increasing the width of the absorbing PML layer.