Fixed grid finite element analysus of solidification

A semi-implicit operator splitting technique is combined with an enthalpy-porosity method to solve both isothermal and temperature range solidification on equal- and unequal-order finite element grids. The performance of the presented algorithm is studied by solving some benchmark problems including a driven cavity flow, free convection (with and without Boussinesq approximation) and a binary alloy solidification. Solutions obtained are free from wiggles and spurious pressure modes and they fit fairly well to the results reported by others. More comprehensive analysis of the algorithm accuracy is given by comparing the obtained results with both the boundary-fitted finite difference front tracking solution and experimental data for the freezing of water in the differentially heated square cavity. Although the calculated volume of the ice meshes well with the experimental data, the detailed structure of flow does not Possible explanations for this incongruity are discussed in the body of this paper.