An Efficient Radial Basis Function Meshfree Local Petrov–Galerkin Method for Modeling the Unidirectional Fully Developed Fluid Flow

In hydrodynamics the applications range of incompressible flows is very wide. In this study, a robust, high order modeling approach is introduced, based on the MLPG meshfree method -based radial basis functions (RBF- MLPG) method, for solving the incompressible flow field. In other words a MLPG meshfree method based on an interpolation function is presented to solve the 2‐D unsteady incompressible fully developed fluid flows. This meshfree method is based on the quartic (4^th order) spline. The method is then compared against the Finite Element Method on a test case of unidirectional fully developed incompressible fluid. The performance of this weight function proved that the quartic (4th order) spline gains the highest accuracy, convergence and efficiency. Finally, it can be concluded that the presented method is formidable for simulating fluid dynamics.