Efficient simulation of two-dimensional time-fractional Navier-Stokes equations using RBF-FD approach

This study is focused on the Navier-Stokes equations. The numerical method employed in this study for solving the Navier-Stokes equations is a meshless approach that combines the radial basis function (RBF) and finite difference (FD) schemes on two-dimensional arbitrary domains. This method, known as radial basis function-generated finite differences (RBF-FD), utilizes the finite difference technique to discretize the time domain and the RBF-FD approximation to discretize the space domain. The RBF-FD method offers several advantages, including high-order convergence rates and the ability to effectively handle sparse node layouts within arbitrary domains. The efficacy and accuracy of the suggested approach are evaluated through the analysis of four unique instances: comprising Taylor-Green vortices, lid-driven cavity flow, backward-facing step flow, and flow around a square cylinder. In the last example, we examined a simulation of air pollution around buildings.