High-resolution, high-order, finite-difference algorithms for computational aeroacoustics

Abstract

Computational Aeroacoustics requires accurate wave propagation over long distances for a wide range of frequencies ([7],[12]). This requirement places a severe demand on numerical algorithms, creating a need for methods with high accuracy and high resolution ([11],[13]). This paper briefly presents high order finite difference methods for the Linearized Euler Equations in both one and two space dimensions. The methods may all be represented as single step explicit algorithms on central stencils. These methods all correctly incorporate the proper wave dynamics of linear constant coefficient hyperbolic systems in one or multiple space dimensions, including propagation along characteristics surfaces for nondiagonalizable systems in two space dimensions. These methods all have the same order of accuracy in time as in space, and they all are stable if the time to space step size ratio is less than one over one plus the maximum mean convection velocity in any single coordinate direction. Two classes of methods will be presented and compared: the first has dispersive truncation error with up to eighth order accuracy in both space and time [3]; the second has diffusive error with up to eleventh order accuracy in both space and time [4].