The “Lab-on-a-Chip” is a micro-scale device which uses fluids as working medium and can handle number of functions such as sample preparation and transfer, separation, bio-sensing and detection. One of the important parts of these devices is micro-mixer, that should blend two fluid species in a short time with desirable mixing quality. Micro-mixers are classified as passive and active. By considering the micro-scale of mixers, turbulence phenomena cannot occur due to dominance of viscous forces, therefore the mixing only depends on molecular diffusion. This thesis consists of two main parts, in the first part algebraic multigrid has been studied and implemented in Rayan (in-house CFD code)....