Implementation of a High-Order Finite Difference Scheme to Model Wave Propagation

Abstract

The large disparity between the time and length scales of an acoustically active flow field, and the ones of the resulting generated acoustic field, is an issue in computational aeroacoustics (CAA). Numerical schemes used to calculate the time and space derivatives in CAA should exhibit a low dispersion and dissipation error. This paper presents the implementation of a high-order finite difference scheme to model CAA problems. The numerical scheme consists of a sixth-order prefactored compact scheme coupled with the 4-6 Low Dispersion and Dissipation Runge-Kutta (LDDRK) time marching scheme. Onesided explicit boundary stencils are implemented and a buffer zone is used to eliminate spurious numerical waves. Results are in good agreement with a 1-D advection equation benchmark problem. This constitutes a preliminary validation for the scheme to explore and investigate the acoustic propagation of sound generated aerodynamically.

Comparison of Optimized High-Order Finite-Difference Schemes for Computational Aeroacoustics

“…The numerical method used at the University of Leicester is the sixth-order prefactored tridiagonal compact scheme of Hixon,14,17 coupled with the classical fourth order time marching scheme, labelled as prefc12rk4. The error and cost maps corresponding to prefc12rk4 are reported in Fig.4a.…”