  In this paper, we present high-performance computing for the BGK model of the
Boltzmann equations with a meshfree method. We use the
Arbitrary-Lagrangian-Eulerian (ALE) method, where the approximation of spatial
derivatives and the reconstruction of a function is based on the weighted least
squares method. We have used the Graphics Processing Unit (GPU) to accelerate
the code and compared with the CPU code. Two and three dimensional driven
cavity problems are solved, where we have obtained the speed up up to 307 times
and 127 times in two and three dimensional cases, respectively.
