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

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.