| An adaptive-grid numerical method for the computer simulation of steady-state, two-dimensional, solid-liquid phase change systems is presented. The grid is designed to delineate the solid-liquid interface using a structured adaptation technique. The fluid flow and thermal fields are solved concurrently using a control-volume finite element method. Of particular interest is the modelling of industrial solidification processes, such as the continuous casting of metal.; The combined adaptive-grid, CVFEM method is formulated for the solution of two-dimensional planar and axisymmetric problems. The proposed method is tested by application to natural convection in closed solid-liquid systems. Test problems in two-dimensional rectangular, cylindrical, and spherical axisymmetric enclosures, are presented.; An analytical solution of an idealized, one-dimensional, steady-state, continuous phase change process is derived. The numerical method is further tested with this analytical solution, and then applied to the continuous casting of aluminum into a cylindrical ingot.{09}Comparisons of the calculated solid-liquid interface geometry with those reported in earlier experimental and numerical studies are encouraging. In addition, the role of natural convection in this casting process is investigated and presented. |
