Solving the Boltzmann Equation on GPU

TL;DR

This paper presents a GPU-accelerated method for solving the Boltzmann equation, combining finite difference and Monte Carlo techniques, significantly reducing computation time for low Mach number flow simulations.

Contribution

It introduces a novel GPU-based approach that accelerates Boltzmann equation solutions, enabling efficient analysis of unsteady low Mach number flows.

Findings

Achieved two orders of magnitude reduction in computation time

Successfully applied to two-dimensional driven cavity flow

Demonstrated viability as an alternative to particle simulations

Abstract

We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference discretization of the free-streaming term with a Monte Carlo evaluation of the collision integral. The efficiency of the code is demonstrated by solving the two-dimensional driven cavity flow. Computational results show that it is possible to cut down the computing time of the sequential code of two order of magnitudes. This makes the proposed method of solution a viable alternative to particle simulations for studying unsteady low Mach number flows.