Solution of the stationary stokes and Navier-Stokes equations using the modified finite particle method in the framework of a least squares residual method

The present work is concerned with the solution of stationary Stokes and Navier-Stokes flows using the Modified Finite Particle Method for spatial derivative approximations and the Least Square Residual Method for the solution of the linear system deriving from the collocation procedure. The combination of such approaches permits to easily handle the numerical difficulty of the inf-sup conditions, without distinguishing between the discretizations of velocity and pressure fields. The obtained results, both in the cases of linear and non-linear flows, show the robustness of the proposed algorithm.