Massively parallel implementation in Python of a pseudo-spectral DNS code for turbulent flows

Abstract: Direct Numerical Simulations (DNS) of the Navier Stokes equations is a valuable research tool in fluid dynamics, but there are very few publicly available codes and, due to heavy number crunching, codes are usually written in low-level languages. In this work a \textasciitilde{}100 line standard scientific Python DNS code is described that nearly matches the performance of pure C for thousands of processors and billions of unknowns. With optimization of a few routines in Cython, it is found to match the performance of a more or less identical solver implemented from scratch in C++. Keys to the efficiency of the solver are the mesh decomposition and three dimensional FFT routines, implemented directly in Python using MPI, wrapped through MPI for Python, and a serial FFT module (both numpy.fft or pyFFTW may be used). Two popular decomposition strategies, slab and pencil, have been implemented and tested.