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

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