Abstarct: Aerodynamic study of flows at low Reynolds for special applications such as micro unmanned underwater vehicles, underwater robots and explorers are interested. In this thesis, an improved progressive preconditioning method named power-law preconditioning method, for analyzing unsteady laminar flows with constant angle of attack and with forced periodical oscillations around hydrofoils is presented. Oscillating unsteady flows have been extensively studied in a variety of contexts. Experimental and numerical studies have explored the dynamics of the wake, details of fish and marine mammal propulsion, the use of oscillating hydrofoils in flow control and ... . In this method, the 2D Navier-Stokes equations modifies by altering the time derivative terms of the governing equations. The preconditioning matrix is adapted from the velocity flow-field by a power-law relation. The governing equation is integrated with a numerical resolution derived from the cell-centered Jameson’s finite volume algorithm and a dual-time implicit procedure is applied for solution of unsteady flows. The stabilization is achieved via the second- and fourth-order artificial dissipation scheme. Explicit four-step Runge–Kutta time integration is applied to achieve the steady-state condition. The computations are presented for unsteady laminar flows around NACA0012 hydrofoil at various angles of attack and Reynolds number. Results presented in the thesis focus on the velocity profiles, lift and drag coefficient and effect of the power-law preconditioning method on convergence speed. The results show satisfactory agreement with numerical works of others and also indicate that using the power-law preconditioner improves the convergence speed and decreases the computational cost, significantly.