Finite element methods for problems with solid‐liquid‐solid phase transitions and free melt surface

Abstract

Modeling and computation of a process with solid‐liquid‐solid phase transitions and a free capillary surface is discussed. The main components of the model are heat conduction, a free melt surface, a moving phase boundary, and its coupling with the Navier‐Stokes equations. We present two different approaches for handling the phase transitions by applying in a FE method, namely an energy conservation based approach, and a sharp interface approach with moving mesh. By combining both methods, we benefit from the advantages of the respective approach. The methods are applied to a problem where material is accumulated by melting the tip of thin steel wires using laser heating. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimization of Engineering Processes Including Heating in Time-Dependent Domains

“…The forward problem with given boundary conditions is discretized by a finite element method which combines a Stefan problem solver with a free-surface Navier-Stokes solver. The latter is based on the Navier code [1], the combined approach is described in more detail in [2,7]. Locally refined (triangular or tetrahedral) meshes are needed in order to approximate the large variations in temperature near the heating zone and the surrounding of the solid-liquid interface sufficiently well, while keeping the overall numerical costs acceptable.…”

Finite element simulation for material accumulation and welding processes including a free melt surface

“…For a welding process, contact angles ω {1,2} are prescribed additionally and a non-melting material Ω S with a non-slip boundary Γ P is introduced. For handling the solid-liquid interface Γ S , an approach based on energy conservation and a sharp interface method are combined, as discussed in [1,3]. To avoid the numerical effort of a complete 3D simulation of the processes, the considered geometry is reduced to a 2D rotational symmetric geometry for a material accumulation process or a 2D cross-section model for a welding process, where the cross-section is taken perpendicular to direction of the heat source movement.…”

“…In this paper, a model presented in [1,2] is used to simulate a material accumulation process and a welding process basing on the numerical approaches presented in [2,3]. For a welding process simulation in a cross-section, a heat source is modeled to approximate heat fluxes in welding direction.…”

Process Window for Forming of Micro Preforms at Different Temperatures

“…These relations lead to the conclusion that for any combination of preform diameter and shaft size a particularly precise process window for forming at different temperatures has to be identified. In order to achieve most fitting results, a mathematical model has been implemented [10].…”