Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. A98-30813 AIAA-98-2221 DEVELOPMENT OF A HIGH-ORDER COMPACT ALGORITHM FOR AEROACOUSTICS EMPLOYING PML ABSORBING BOUNDARIES Peter W. TenPas*, Stephen E. Schwalm + and Ramesh K. Agarwal** * >+ Department of Mechanical Engineering University of Kansas Lawrence, Kansas 66044-7526 ** Aerospace Engineering Department National Institute for Aviation Research Wichita State University Wichita, Kansas 67260-0093 ABSTRACT A finite-difference method for solving the two- dimensional 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 non- physical reflections at the boundaries of the domain. The boundary error can be controlled or eliminated by increasing the width of the absorbing PML layer. Copyright © 1998 by P.W. TenPas. Published by the Confederation of European Aerospace Societies, with permission. * Associate Professor, Member AIAA """Undergraduate Research Assistant ** Bloomfield Distinguished Professor, Fellow AIAA INTRODUCTION Numerical simulation of aerodynamic sound propagation places severe requirements on the accuracy of the computational process. Research in computational aeroacoustics (CAA) is directed toward the development of procedures that are capable of high resolution and are also robust and computationally efficient. Tarn 1 has recently published a survey of the field. The list of technical issues includes but is not limited to: high frequency wave resolution on coarse grids, proper representation of the far-field boundary conditions, integration over many cycles or long times and acceleration of convergence to steady-state. Computational resources such as processor speed and storage space place a practical limit on the number of grid points used in a numerical simulation. To study high frequency wave propagation on a relatively coarse grid the numerical method used must be able to accurately resolve waves with as few as 6 node points per wavelength. Low-order finite-difference methods exhibit large dispersion errors when applied on coarse grids. Conventional high-order methods yield more accurate results at the expense of incorporating a larger number of nodes in the difference stencil. This adds to the processing time, and more importantly the wider stencils are more difficult to apply near boundaries. The formal order of accuracy and the number of points in the stencil are not reliable measures of the resolution of a particular scheme. The compact schemes described by Lele 2 achieve higher-order accuracy without greatly expanding the 104