A highly accurate GPU Lattice Boltzmann method with directional interpolation for the probability distribution functions

In this article, a highly accurate and graphics processing unit (GPU)-accelerated Lattice Boltzmann Method (LBM) is presented. The methodology is derived from a combination of conventional and recent LBM algorithms, mainly focusing on reducing the computational time, memory allocation, and complexity of existing algorithms. The general implementation focuses on accelerating the overall methodology using GPGPU technology based on Compute Shaders from OpenGL and avoids the storage of the distribution function components to reduce the memory allocation size. Furthermore, an efficient spatial interpolation of the probability distribution function components is described, based on a directional interpolation, without unnecessary control points for the reconstruction of virtual nodes data. The present methodology, tested for spatial accuracy via two- and three-dimensional Lid-Driven Cavity benchmark cases, shows excellent agreement with the results reported in the literature. Additionally, time efficiency is analyzed by comparing different configurations for the construction of virtual streaming points.