NadiaSpectral is a computer code that simulates non-stationnary 3D flow between two walls. This code was initially developed during the PHD thesis of my student Henry Pascal in 1995, following an idea of Lionel LePenven, to study a wall-bounded Compressed Turbulence. The numerical method is based on a general orthogonal decomposition proposed by Le Penven et Buffat (2012) for solenoidal vector fields expressed in terms of projections of the velocity and vorticity fields on an arbitrary direction in space. For doubly-periodic flow with one direction of inhomogeneity (normal direction), Buffat et al. (Computer & Fluids 2011) derived an explicit form of this decomposition using the Helmholtz-Hodge theorem and showed that any divergence-free velocity field can be written as an L2 orthogonal sum of two solenoidal velocity fields depending on the normal velocity and vorticity components respectively. For wall bounded flow this decomposition is linked to the Orr-Sommerfeld and Squire modal decomposition of the linear stability theory (Buffat and Le Penven POF 2012).

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