Phase-field modeling of dry snow metamorphism
Snow on the ground is a complex three-dimensional porous medium consisting of an ice matrix formed by sintered snow crystals and a pore space filled with air and water vapor. If a temperature gradient is imposed on the snow, a water vapor gradient in the pore space is induced and the snow microstructure changes due to diffusion, sublimation, and resublimation: the snow metamorphoses. The snow microstructure, in turn, determines macroscopic snow properties such as the thermal conductivity of a snowpack. We develop a phase-field model for snow metamorphism that operates on natural snow microstructures as observed by computed X-ray micro-tomography. The model takes into account heat and mass diffusion within the ice matrix and pore space, as well as phase changes at the ice-air interfaces. Its construction is inspired by phase-field models for alloy solidification, which allows us to relate the phase-field to a sharp-interface formulation of the problem without performing formal matched asymptotics. To overcome the computational difficulties created by the large difference between diffusional and interface-migration time scales, we introduce a method for accelerating the numerical simulations that formally amounts to reducing the heat- and mass-diffusion coefficients while maintaining the correct interface velocities. The model is validated by simulations for simple one- and two-dimensional test cases. Furthermore, we perform qualitative metamorphism simulations on natural snow structures to demonstrate the potential of the approach.