A trust region approach for numerical modeling of non-isothermal phase change

An efficient enthalpy-based numerical approach is introduced for solving heat transfer problems with non-isothermal phase change. The goal of this model is to simulate permafrost thaw rates, understand the significant effects of climate change on permafrost, and assess the reciprocal effects of permafrost thaw on climate. In order to simulate permafrost over time spans of several years, a robust and efficient model is required. In the present setting, the heat transfer problem is converted to a minimization problem, in which we minimize a potential function that characterizes the governing heat transfer PDE within a time discrete framework. The use of the trust region minimization algorithm proves desirable due to the highly non-linear energy functional which also involves non-convex terms induced by phase change. Results obtained show satisfactory agreement with existing analytical solutions. Moreover, the grid and time step convergence studies conducted to examine the dependence of the solution on mesh and time step sizes indicate robust convergence rates. This is the first application of trust region energy minimization algorithm in permafrost simulation.