Numerical Evaluation of the Compact Green's Function for the Solution of Acoustic Flows

Due to the relatively tiny length scales involved, complex acoustic flows are not always suitable for traditional CFD codes. This paper develops a robust, semi-analytical numerical method for predicting sound fields based on the calculation of the compact Green’s function over a grid of source-observer positions. These calculations often involve singular functions, hence variations of the method are applied to several different 2D problems to investigate the impact of any singularities on the solution. The effect of grid point density and other parameters on execution time and accuracy are explored including the effects of approximating curved geometries using a number of straight lines. Comparison to known analytical solutions for the 2D problems is used to assess the accuracy of the method. For a typical application, we compute the far-field sound generated by a simple source in the vicinity of a compact, ‘2D’ fan blade in a duct. The current method demonstrates calculation of the compact Green’s function both accurately and robustly by avoiding the mapping from unbounded domains and the evaluation of potential models containing singularities. Both are seen as sources of error which have a widespread impact.