2023/06/02 by Dawid Strzelczyk, Strzelczyk, Dawid, Maciej Matyka +1
Computer Science · Engineering · #Aerosol Filtration and Electrostatic Precipitation #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Generative Adversarial Networks and Image Synthesis #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2306.01525
openalex publication_date 2023/06/02 · openalex created_date 2023/06/07 · openalex updated_date 2026/07/28
The Meshless Lattice Boltzmann Method (MLBM) is a numerical tool that relieves the standard Lattice Boltzmann Method (LBM) from regular lattices and, at the same time, decouples space and velocity discretizations. In this study, we investigate the numerical convergence of MLBM in two benchmark tests: the Taylor-Green vortex and annular (bent) channel flow. We compare our MLBM results to LBM and to the analytical solution of the Navier-Stokes equation. We investigate the method's convergence in terms of the discretization parameter, the interpolation order, and the LBM streaming distance refinement. We observe that MLBM outperforms LBM in terms of the error value for the same number of nodes discretizing the domain. We find that LBM errors at a given streaming distance δx and timestep length δt are the asymptotic lower bounds of MLBM errors with the same streaming distance and timestep length. Finally, we suggest an expression for the MLBM error that consists of the LBM error and other terms related to the semi-Lagrangian nature of the discussed method itself.