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We present a pseudo-spectal Navier-Stokes solver for plane parallel flows(Couette/Poiseuille), that has been developed on the MATLAB programminglanguage. The code performs direct numerical simulations (DNSs) of turbulencein 3 dimensions at low Reynolds numbers ($Re_{\tau} \approx 40-180 $), using aprogramming structure that mainly employs matrix multiplications to solve theNavier-Stokes equations. The novelty of this DNS code lies on the vectorizationof the required operations to simultaneously advance in time an ensemble offlow realizations and the utilization of graphics processing unit (GPU)computational resources, which offers a significant reduction of running timefor simulations with adequately resolved viscous scales.

A vectorized Navier-Stokes ensemble direct numerical simulation code for plane parallel flows