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

TL;DR

This paper introduces a GPU-accelerated, vectorized DNS code for simulating low-Reynolds-number plane parallel flows, enabling faster turbulence simulations by leveraging matrix operations and ensemble computations.

Contribution

The novel aspect is the development of a MATLAB-based, vectorized DNS solver that efficiently utilizes GPU resources for ensemble turbulence simulations in plane parallel flows.

Findings

Significant reduction in simulation time using GPU acceleration.

Successful simulation of turbulence at low Reynolds numbers.

Efficient ensemble computation achieved through vectorization.

Abstract

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 ($Re_{\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.