AN EFFICIENT, TWO-DIMENSIONAL IMPLEMENTATION OF THE FFOWCS WILLIAMS AND HAWKINGS EQUATION

By D. Lockard. 2000

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Direct computation of the noise radiated by a subsonic cavity flow and application of integral methods (2003, methodology): “For bidimensional geometries, it is more convenient to resolve this equation in the spectral domain [ 40 ,41].”
Unstructured Large-Eddy Simulations of Supersonic Jets (2017, methodology): “For the far-field noise solver, the frequency-domain formulation [36,37] of the FW-H equation is a robust and efficient method ideally suited for jet aeroacoustics (including forward-flight effects).”
Convective effects and the role of quadrupole sources for aerofoil aeroacoustics (2012, methodology): “Following the development of Lockard (2000), the FWH formulation can be written as [p̂′H(f )] = − ∫ f=0 [ iωQ̂(y)Gc(x, y)+ F̂i(y)∂Gc(x, y) ∂yi ] dS − ∫ f>0 T̂ijH(f ) ∂2Gc(x, y) ∂yi∂yj dV, (3.1) where ω is the angular frequency, f = 0 represents the FWH surface and H(f ) is the Heaviside function…”
Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets (2018, methodology): “The framework is composed of the pre-processing meshadaptation tool “Adapt”, the compressible flow solver “Charles,” and post-processing tools for far-field noise predictions based on an efficient massively-parallel implementation of the frequency-domain permeable formulation (Lockard 2000) of the F”