A study of the accuracy and stability of high-order compact difference methods for computational aeroacoustics

A study of the accuracy of compact difference operators is undertaken to determine the savings realized by use of high-order pentadiagonal difference operators for the numerical solution of selected multi-dimensional problems in aeroacoustics. The use of Low-Dissipation and Low-Dispersion Runge-Kutta (LDDRK) integration is also advocated to minimize numerical error for a given step size.; A combined stability analysis for spatial discretization using the compact difference operator and the alternating-step LDDRK integration scheme is presented for the one-dimensional linear convection equation and periodic boundary conditions.; PML boundary conditions for absorbing acoustic and vortical waves normal to the computational domain are implemented here. A linear stability analysis is used in the PML zones to determine optimal values of the damping coefficient to minimize growth instabilities that are inherent to the PML equations for mean flow normal to the PML boundaries.; For the 3-D case, use of the pentadiagonal compact scheme resulted in a 53% reduction in the spatial grid requirement (and associated memory space) compared to the tridiagonal scheme. The decrease in actual computational time is 27% by using CD05/10 compared to CDO3/8 for the same level of solution accuracy. These reductions are in addition to the 50% savings in CPU time achieved by adopting the LDDRK5/6 time-integration as opposed to traditional fourth-order Runge-Kutta integration.