A concise python implementation of the lattice Boltzmann method on HPC for geo-fluid flow

Abstract

SUMMARY The lattice Boltzmann method (LBM) is a method to simulate fluid dynamics based on modelling distributions of particles moving and colliding on a lattice. The Python scripting language provides a clean programming paradigm to develop codes based on the LBM, however in order to reach performance comparable to compiled languages, it needs to be carefully implemented, maximizing its vectorized tools, mostly integrated in the NumPy module. We present here the details of a Python implementation of a concise LBM code, with the purpose of offering a pedagogical tool for students and professionals in the geosciences who are approaching this technique for the first time. The first half of the paper focuses on how to vectorize a 2-D LBM code and show how if carefully done, this allows performance close to a compiled code. In the second part of the paper, we use the vectorization described earlier to naturally write a parallel implementation using MPI and test both weak and hard scaling up to 1280 cores. One benchmark, Poiseuille flow and two applications, one on sound wave propagation and another on fluid-flow through a simplified model of a rock matrix are finally shown.