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 boundary conditions allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions, Thus, the task of designing a complex multidimensional scheme with approximate boundary conditions 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 boundary 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 second order for algorithmic simplicity as the Crank-Nicolson scheme, The robustness and accuracy of the scheme and the validity of the system decoupling are demonstrated through a series of numerical experiments and comparisons with published results, including the recent Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, benchmark problems of acoustic and convective wave propagation in Cartesian and cylindrical domains and reflection at stationary and/or moving boundaries.