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A numerical method for the direct numerical simulation of the incompressible Navier–Stokes equations in rectangular geometries is presented. The method implement the MPI Standard to the engine introduced by M.Quadrio and P.Luchini. The method is based on Fourier expansions in the homogeneous directions and fourth-order accurate, compact finite-difference schemes over a variable-spacing mesh in the wall-normal direction.
Two different versions of the solver have been developed, based on the domain decomposition. In the first the domain is decomposed through 1D (Slab), while in the second version a 2D (Pencil ) decomposition is used. The performance of these versions, in terms of speedup and parallel efficiency, have been compared against each other by varying number of cores, processor architecture and mesh size, highlighting the scalability benefits which derives from the latter decomposition method as soon as the mesh dimensions becomes important. The principal drawback of the code has been highlighted, together with the possible solution to improve the global efficiency of the code. To manage the decomposition we rely on the APIs present in fftMPI, developed by Steve Plimpton at Sandia National Laboratories.
The results of a simulation at Retau=1000 and a preliminary simulation at Retau=2000 are presented.