Development of a compatible computational fluid dynamics procedure to investigate rigid and fixed/free coastal and offshore structures hydrodynamics in a time-dependent one/two phase flow of viscous incompressible fluids is presented. Differential governing equations are discretised using finite volume approach based on a colocated arrangement. The conservation equations for mass and momentum are solved using a fractional step method. In conjunction, free surface is simulated using a volume method. An overlapping mesh system is implemented to deal with a two-dimensional computational domain including a non-uniform background mesh of Cartesian cells as well as an overset mesh of quad cells. According to the complete assessment of the code developed based on the algorithm, there is a robust tool to deal with hydrodynamics where extension to three dimensions is straightforward, as well. Although many two-dimensional problems can be solved, but the code must be developed for three dimensions. In addition, turbulence is not considered in the present formulation and left for future researches. A simple non-conservative approach to transfer all two-phase flow variables is introduced. Besides, Algebraic sets of equations extracted from different meshes for each variable are solved simultaneously to construct a strong coupling. The final algorithm is a new and appropriate combination, as well.