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Abstract

Moving boundary problems are mathematically challenging because the domain itself and its boundary are part of the solution. An elegant way to solve these problems are the so-called diffuse interface methods, where the moving boundary is treated as a volume with small but finite thickness separating two distinct materials. Applications are phase transformations in crystalline materials, motion of droplets and gases, viscous fingering of flow in porous media and crack growth in solids. The talk will give an introduction to the theoretical background of diffuse interface models with special emphasis on Phase-field and Lattice-Boltzmann methods. These methods are derived thermodynamically consistently from a free energy formulation including a CALPHAD type description of the stability of phases. Examples of microstructure evolution in metals and polymers are presented. Finally perspectives to apply these methods to Lithospheric deformation will be outlined.