High Order Numerical Simulation of Sound Generated by the Kirchhoff Vortex

Abstract

An improved high order finite difference method for low Mach number computational aeroacoustics (CAA) is described. The improvements involve the conditioning of the Euler equations in perturbation form to minimize numerical cancellation error, and the use of a stable non-dissipative sixth-order central spatial differencing for the interior points and third-order at the boundary points. The spatial difference operator satisfies the summation-by-parts property to guarantee strict stability for linear hyperbolic systems. Spurious high frequency oscillations are damped by a third-order characteristic-based filter. The objective of this paper is to apply these improvements in the simulation of sound generated by the Kirchhoff vortex.