A stabilized meshless method for the solution of the lagrangian equations of newtonian fluids

In this article we present numerical methods for the approximation of incompressible flows. We have addressed three problems: the stationary Stokes’ problem, the transient Stokes’ problem, and the general motion of newtonian fluids. In the three cases a discretization is employed that does not require a mesh of the domain but uses maximum entropy approximation functions. To guarantee the robustness of the solution a stabilization technique is employed. The most general problem, that of the motion of newtonian fluids, is formulated in lagrangian form. The results presented verify that stabilized meshless methods can be a competitive alternative to other approached currently in use