A direct velocity-pressure coupling Meshless algorithm for incompressible fluid flow simulations

A localized radial-basis function (RBF) Meshless algorithm, with a direct velocity-pressure coupling scheme, is presented for fluid flow simulations. The proposed method is a combination of several efficient techniques found in different Computational Fluid Dynamic (CFD) procedures and has very low numerical diffusion. The fundamental idea of this method lays on several important inconsistencies found in three of the most popular techniques used in CFD, segregated procedures, streamline-vorticity formulation for 2D viscous flows, and the fractional-step method, very popular in Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). The proposed scheme uses the classical segregated point distribution for all primitive variables, and performs all necessary interpolations with the accurate RBF technique. The viscous term is estimated using standard second order finite differences, while the convection term is discretized using the low-diffusion flux limiters. The velocity-pressure coupling is performed with the flow equations in their original form, and using a direct velocity-pressure coupling scheme. This way of solving the flow equations has no approximations in the boundary conditions. The method is validated with the 2D lid-driven cavity problem and very good agreement is found with classical data.