An interface-tracking control-volume finite-element method for melting andsolidification problems - Part I: Formulation

An interface-tracking method is presented to solve two-dimensional convecti on-dominated melting and solidification problems in enclosures of arbitrari ly geometry. The control-volume finite-element method (CVFEM) is applied to moving-boundary problems using an adaptive moving-grid model based on unst ructured triangular grids. At every sampling instant, the liquid-solid inte rface is explicitly resolved by the numerical grid. A suitable chosen mesh velocity is introduced directly into the governing equations minimizing gri d deformation in the vicinity of thp moving interface. Additionally, the im plementation of local grid adaption algorithms (refinement, coarsening, rel axation) prevents undesirable changes of mesh resolution due to the moving interfaces. Thus, even in problems involving large-scale interface motion o r boundary deformation, a continuous high-quality grid can be preserved. Fu rthermore, the adaptive procedure is able to produce highly graded meshes t hat can be "online" locally adapted to react on changing physics in Be simu lation of an unsteady, process. Numerous test calculations for verification of the proposed method are presented in part II.