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This article presents a numerical algorithm using the Meshless Local PetrovGalerkin (MLPG) method for numerical simulation of unsteady incompressible flows, governed by the Navier–Stokes equations via the stream function–vorticity (ψ–ω) formulation. The driven flow in a square cavity is used as the model problem. The present method is a truly meshless method based only on a number of randomly scattered nodes. The multiquadrics RBFs are employed for constructing trial functions in the local weighted meshless local Petrov–Galerkin method. The present numerical algorithm is based on a local weighted residual method with the Heaviside step function as the test function over a local subdomain. The efficiency, accuracy and robustness of the numerical algorithm are demonstrated by the standard driven cavity. It is observed that the obtained results agreed very well with the results of Ghia. Therefore the ability and accuracy of the present numerical algorithm was presented by solving the standard driven cavity flow problem with reasonable accuracy when compared to solutions obtained by Ghia. In other words the benchmark computations indicate that the MLPG Meshless method is very effective in the simulation of fluid flow problems.

A MLPG Meshless Method for Numerical Simulation of Unsteady Incompressible Flows