ABSTRACT:

We present a heterogeneous domain decomposition approach for solving nonlinear heat conduction for a snow-soil model in Arctic environments. The snow and soil domains are treated as distinct physical domains, each described by a separate nonlinear heat equation with distinct nonlinear laws for material properties. These two models are coupled across their interface by ensuring the continuity of temperature and the conservation of heat flux. The coupled system is solved iteratively with a Dirichlet to Neumann approach, where the snow and soil models are solved independently, updating the interface conditions within a Richardson scheme until convergence is achieved. We show the basics of analysis, compare with Schur complement calculations, and with the monolithic approach.