A meshless lattice Boltzmann numerical method has been developed. The collision and streaming operators of the lattice Boltzmann equation have been separated, as in the usual lattice Boltzmann models. While the purely local collision equation has remained the same, we have rewritten the streaming equation as a pure advection equation and discretized the resulting partial differential equation using the Lax-Wendroff scheme in time and the meshless local Petrov-Galerkin scheme based on augmented radial basis functions in space. The proposed method has been implemented on a computer code. Some well-known benchmark fluid flow problems, namely the plane and circular Couette flows, the three-dimensional lid-driven cavity flow, and the impulsively started cylinder flow have been simulated for the validation of the proposed method. Excellent agreements with analytical solutions or with previous experimental and numerical results in the literature have been observed in all the simulations. Although the computational resources required for the new meshless method per node are higher compared to that of the standard lattice Boltzmann method, it has been shown that for cases in which the total number of nodes is significantly reduced, such as flow in packed beds, the present method actually outperforms the standard lattice Boltzmann method. ? Keywords: Lattice Boltzmann, Meshless method, Fluid flow, Complex geometry ?
