Methods for the direct and large-eddy simulation of lfows about turbomachinery blading are presented. For incompressible flows, both direct and large-eddy simulation require the solution of a Poisson equation for pressure, which is frequently the main source of computational expense in simulations within complex boundaries. Marked computational advantages are described for a flow which is periodic in one dimension through the use of Fourier transform the Poisson equation for the pressure field, decomposing the problem into a set of two-dimensional problems of similar type. We demonstrate that even when a complex geometry and body-fitted curvilinear coordinates are used inthe other two dimensions, for instance to solve flow around a 2D turbine blade or blade row, the resulting Fourier-transformed 2D problems are much more efficiently solved than the 3D problem by iterative means.
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