Abstarct: Formation of ice on a solid surface with a temperature lower than water freezing temperature, as well as ice boundary formation has great influence on different aspects and it is of great importance in the freezing period to determine ice boundary position and the effect of liquid phase flow on the formation of ice boundary. Ice formation is a complex process involving heat and mass transfer. Analytical solution for this transient and complicate phenomena is impossible and expensive laboratory instruments are required to understand the process of ice formation. Typically enthalpy-porosity method is used for simulating the process of freezing materials with the same thermophysical characteristics in both liquid and solid phases. In the present study, this method has been developed by defining and applying functions of thermophysical characteristics and developing a continuous function presenting liquid volume fraction, considering the major changes in water thermophysical characteristics during the formation of ice. The results obtained from the proposed simulation method are compared to the experimental and numerical ones for the case of freezing inside a cubic cavity. Formation of two circulations and maintaining the solid phase boundary orthogonal to the bottom wall during the ice growth process emphasizes success of this model and generated code in open source software OpenFOAM compared to similar researches as well. The comparison shows a better solid boundary formation prediction and also 3% average improvement in results with respect to recent numerical simulations.