Sea ice seasonally to interannually forms a thermal, chemical, and physical boundary between the atmosphere and hydrosphere over tens of millions of square kilometers of ocean. Its presence affects both local and global climate and ocean dynamics, ice shelf processes, and biological communities. Accurate incorporation of sea ice growth and decay, and its associated thermal and physiochemical processes, is underrepresented in large‐scale models due to the complex physics that dictate oceanic ice formation and evolution. Two phenomena complicate sea ice simulation, particularly in the Antarctic: the multiphase physics of reactive transport brought about by the inhomogeneous solidification of seawater, and the buoyancy driven accretion of platelet ice formed by supercooled ice shelf water onto the basal surface of the overlying ice. Here a one‐dimensional finite difference model capable of simulating both processes is developed and tested against ice core data. Temperature, salinity, liquid fraction, fluid velocity, total salt content, and ice structure are computed during model runs. The model results agree well with empirical observations and simulations highlight the effect platelet ice accretion has on overall ice thickness and characteristics. Results from sensitivity studies emphasize the need to further constrain sea ice microstructure and the associated physics, particularly permeability‐porosity relationships, if a complete model of sea ice evolution is to be obtained. Additionally, implications for terrestrial ice shelves and icy moons in the solar system are discussed.