A variational construction of anisotropic mobility in phase-field simulation

In the phase-field modeling of the mezoscopic morphology and microstructure evolution in many material processes, an anisotropic mobility is often needed that depends on the interfacial normal direction. It is a challenge to define the anisotropic mobility function on the whole simulation domain while the interfacial normal can only be meaningfully determined on the interface. We propose a variational approach for the construction of a smoothened mobility function that mimics the prescribed anisotropic mobility on the interface and extends smoothly to the whole simulation domain. Some theoretical analysis of the proposed method are made to ensure its validity and to provide hints on the effects and the choices of various parameters. An iterative scheme for the numerical solution of the variational problem is also described. Several numerical tests are presented to illustrate the effect of a smoother anisotropic mobility on the interfacial dynamics, and the advantage over using a cutoff mobility.