An overview of high-order finite difference schemes for computational aeroacoustics

One of the problems in computational aeroacoustics (CAA) is the large disparity between the length and time scales of the flow field, which may be the source of aerodynamically generated noise, and the ones of the resulting acoustic field. This is the main reason why numerical schemes, used to calculate the timeand space-derivatives, should exhibit a low dispersion and dissipation error. This paper focuses on the evaluation of a number of numerical schemes. The methods that are included, are a representative selection of the most commonly used numerical schemes in CAA. Four different spatial schemes are analyzed:(1) a standard 7-point central difference scheme,(2) a standard 9-point central difference scheme,(3) the Dispersion-Relation-Preserving scheme and (4) a 9-point optimized central difference scheme. For the time integration, six different Runge-Kutta methods are analyzed:(1) a standard 5-stage Runge-Kutta,(2) a 5-stage optimized Runge-Kutta,(3) the 5-stage low-dispersion low-dissipation Runge-Kutta,(4) a standard 6stage Runge-Kutta,(5) a 6-stage optimized Runge-Kutta and (6) the 6-stage low-dispersion low-dissipation Runge-Kutta. The different methods are tested for a 1D-propagation problem.