A numerical method based on finite element approximations for the simulation of macrosegregation during solidification processes is presented. In order to describe carefully the boundary layer close to the dendrite tips, where solutal variations are initiated, two different discretizations in space are introduced. A fixed, coarse and global finite element mesh is used at the scale of the casting, whereas a fine mesh evolving with the mushy zone is created by subdivision of the coarse elements which belong to the critical region. For the physical model, average conservation laws for energy, mass, momentum and solute are used. The coupled system of partial differential equations is solved using the two finite element discretizations as follows. At each time step, the resolution of the heat equation at the macroscopic level determines the position of the mushy zone and thus the elements, which need refinement. Fluid flow is then computed on the coarse grid, followed by the resolution within the refined region. Finally, the solute conservation equations are solved by applying a substructuring iterative method using the two discretizations and the coarse and fine approximations of the velocity field. The interpolation and restriction on the boundary of the mushy zone, which allow the passage from the coarse to the fine grid and vice versa, respectively, are done in a conservative way. This adaptive, multiple grid method has been applied to two test cases: fluid flow in a solidifying channel and solute transport in a rectangular cavity. It is shown that a better accuracy can be obtained while limiting the computation time.
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