IMPLICIT HIGH-ORDER COMPACT ALGORITHM FOR COMPUTATIONAL ACOUSTICS

Accurate solution of the linearized, multidimensional Euler equations for aeroacoustics as a system of simple wave equations is demonstrated , If organized, this system has unambiguous, easily implemented bounda ry conditions allowing waves of same group speeds to pass through nume rical boundaries or comply with wall conditions, Thus, the task of des igning a complex multidimensional scheme with approximate boundary con ditions reduces to the design of accurate schemes for the simple wave equation, In particular, an implicit compact finite difference scheme and a characteristically exact but numerically nth-order-accurate boun dary condition are used, This low-dispersion scheme has a third-order spatial accuracy for various types of nonuniform meshes, fourth-order accuracy on uniform meshes, and by choice a temporal accuracy of secon d order for algorithmic simplicity as the Crank-Nicolson scheme, The r obustness and accuracy of the scheme and the validity of the system de coupling are demonstrated through a series of numerical experiments an d comparisons with published results, including the recent Institute f or Computer Applications in Science and Engineering, NASA Langley Rese arch Center, benchmark problems of acoustic and convective wave propag ation in Cartesian and cylindrical domains and reflection at stationar y and/or moving boundaries.