Barik N.B.; Sekhar T.V.S.2025-02-1720203http://dx.doi.org/10.1080/10407790.2020.1803611https://idr.iitbbs.ac.in/handle/2008/3073In this article, we developed a computationally efficient multilevel local radial basis function (RBF-FD) mesh-free algorithm. The algorithm provides a new strategy to get good order of accuracy with less computational time, which is most important in the present world. The main idea is the layer-by-layer calculation and then layer-by-layer correction from coarsest level to finest level node points. Numerical experiments are presented to verify the accuracy and efficiency of our developed algorithm with two-dimensional Poisson equation and vorticity�stream function of the incompressible Navier�Stokes equations. The flow inside a lid-driven cavity constitutes a classical benchmark problem, due to its unique boundary conditions that allow comparing any new method�s efficiency for solving Navier�Stokes equations for internal flows. Numerical results are presented through the figures and tables to demonstrate accuracy, efficiency, and convergence of the method. The developed scheme saves at least 60% of CPU time for Poisson equation and 59% of the CPU time for Navier�Stokes equation than the usual local RBF method. The iteration matrix of the proposed local RBF method satisfies the necessary and sufficient condition for convergence. � 2020 Taylor & Francis Group, LLC.Article