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In this paper, details of a numerical model development for simulation of fluid flows with moving free surface are presented. The unsteady incompressible Navier-Stokes equations on a fixed grid system are used to obtain velocity and pressure values in the computational domain and volume of fluid (VOF) method is used to determine free surface location. In order to reduce numerical smearing and increase accuracy of numerical modeling of fluid flow with moving free surface, a new free surface-tracking method is proposed. The proposed method is a combination of genetic algorithm and free surface tracking method based on donor and acceptor scheme. The specification of the new combinational method can be summarized in determining orientation vector and plane constant to represent the free surface orientation in each cell. The proposed algorithm can be easily used in any unstructured grids. In this method, the fluid flow equations are explicitly discretized with the finite volume method and the projection method is used to determine the velocity and pressure magnitude in computational domain. Validity of the new solution algorithm is demonstrated through its application to the dam break and the bore motion examples. [ABSTRACT FROM AUTHOR]