Regarding Numerical Considerations for Computational Aeroacoustics

A Numerical Validation of a High-Order Finite-Difference Compact Scheme for Computational Aeroacoustics

“…The location of this cross-section is as specified in the first workshop on benchmark problems in CAA. 1 The numerical solution, shown by the the squares (2), is well-matched to the analytical solution, shown by the solid line. There is no appreciable departure between the two solutions at the right boundary of the plot, where the predictions are closest to the right computational boundary and are therefore more likely to start to suffer from numerical boundary effects.…”

“…Contour levels 0.01 and 0.05 have been selected in accordance to the guidelines of the first workshop on benchmark problems in CAA. 1 The analytical reference solution (−) has been overlaid on the numerical predictions (−−) and there is a consistent good overlap between the two. From the non-dimensional density field, a cross-section of the density perturbation distribution has been extracted along x = y line.…”

“…The predictions show that the numerical results are in very good agreement with the reference analytical solution. In performing such tests the guidelines of the first workshop on benchmark problems in CAA 1 have been followed as rigorously as possible, to provide a solid validation statement. The absence of spurious numerical features in areas of multiple wall reflections is a novel test to verify the absence of numerical artefacts where a more non-linear interaction of larger amplitudes occurs at the corner of the computational domain, which is usually a difficult area to treat with adequate numerical conditions.…”

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

“…7 This problem asks for the solution at a nondimensional time=400 of the 1-D linear convection equation:…”

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

“…The seminal work of Lele 4 on high-order finite-difference schemes for computational aeroacoustics encouraged active work in this field, documented by four computational aeroacoustic workshops on benchmark problems [5][6][7][8] and related literature. 9 The early work focussed on achieving a high-order formal accuracy, as determined by the truncation error of the approximate Taylor series expansion of the differential operators.…”