Study of the convergence of the Meshless Lattice Boltzmann Method in Taylor-Green and annular channel flows

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 $\delta x$ and timestep length $\delta t$ 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

Two algorithms for fast 2D node generation: application to RBF meshless discretization of diffusion problems and image halftoning

Mesh generation techniques for traditional mesh based numerical approaches such as FEM and FVM have now reached a good degree of maturity. There is no such an acknowledged background when dealing with node generation techniques for meshless numerical approaches, despite their theoretical simplicity and efficiency; furthermore node generation can be put in connection with some well-known image approximation techniques. Two node generation algorithms are here proposed and employed in the numerical solution of 2D steady state diffusion problems by means of a local Radial Basis Function (RBF) meshless method. Finally, such algorithms are also tested for greyscale image approximation through stippling