Despite of passing many years from invention of Computational Fluid Dynamics (CFD), simulation of the fluid-solid interfaces and free surfaces are still completely challenging and progressive problems. In addition knowing and understanding nanotechnology huge applications,modeling of nano-fluids have been became a priority for researchers. Adding importance of Non-Newtonian fluids (especially polymeric solutions) to this two subjects, triangle topics of this research becomes vivid. In this research tried to consider and examine behavior of Newtonian,Generalized-Newtonian, Viscoelastic and nano-filled viscoelastic fluids in one and two phase mediums. we followed mesh free methods which are...