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Abstract
An interface-tracking method is presented to solve two-dimensional convection-dominated melting and solidification problems in enclosures of arbitrarily geometry. The control-volume finite-element method (CVFEM) is applied to moving-boundary problems using an adaptive moving-grid model based on unstructured triangular grids. At every sampling instant, the liquid-solid interface is explicitly resolved by the numerical grid. A suitable chosen mesh velocity is introduced directly into the governing equations minimizing grid deformation in the vicinity of the moving interface. Additionally, the implementation of local grid adaption algorithms (refinement, coarsening, relaxation) prevents undesirable changes of mesh resolution due to the moving interfaces. Thus, even in problems involving large-scale interface motion or boundary deformation, a continuous high-quality grid can be preserved. Furthermore, the adaptive procedure is able to produce highly graded meshes that can be "online" locally adapted to react on changing physics in the simulation of an unsteady process. Numerous test calculations for verification of the proposed method are presented in part II.