High-performance computing for the BGK model of the Boltzmann equation with a meshfree Arbitrary Lagrangian-Eulerian (ALE) method

TL;DR

This paper introduces a GPU-accelerated mesh-free ALE method for simulating the BGK model of the Boltzmann equation, achieving significant speed-ups over CPU implementations in 2D and 3D cavity problems.

Contribution

It develops a high-performance GPU implementation of a mesh-free ALE method for the BGK model, demonstrating substantial computational acceleration.

Findings

Achieved several orders of magnitude speed-up with GPU over CPU.

Successfully solved 2D and 3D cavity problems.

Validated the efficiency of the mesh-free ALE approach.

Abstract

In this paper, we present high-performance computing for the BGK model of the Boltzmann equation with a mesh-free method. For the numerical simulation of the BGK equation we use an Arbitrary-Lagrangian-Eulerian (ALE) method developed in previous work, where the approximation of spatial derivatives and the reconstruction of a function is based on the weighted least squares method. A Graphics Processing Unit (GPU) is used to accelerate the code. The result is compared with sequential and parallel versions of the CPU code. Two and three-dimensional driven cavity problems are solved, where a speed-up of several orders of magnitude is obtained compared to a sequential CPU simulation.