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This paper presents a novel fully-automatic remeshing procedure, based on the level-set method and Delaunay triangulation, to model three-dimensional boundary problems and generate a new conformal body-fitted mesh. The proposed methodology is applied to long-term in-flight ice accretion, which is characterized by the formation of extremely irregular ice shapes. Since ice accretion is coupled with the aerodynamic flow field, a multi-step procedure is implemented. The total icing exposure time is subdivided into smaller time steps, and at each time step a three-dimensional body-fitted mesh, suitable for the computation of the aerodynamic flow field around the updated geometry, is generated automatically. The methodology proposed can effectively deal with front intersections, as shown with a manufactured example.