A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation

Abstract. The accurate simulation of heat transfer with phase change is a central problem in cryosphere studies. This because the non-linear behaviour enthalpy as function temperature can prevent thermal models snow, ice, and frozen soil from converging to correct solution. Existing numerical techniques rely on increased temporal resolution trying keep corresponding errors within acceptable bounds. Here, we propose an algorithm, originally applied solve water flow soils, method these integration issues guaranteed convergence conservation energy for any time step size. We review common modelling approaches, focusing fixed-grid soil. Based this, develop conservative formulation governing equation outline problems alternative formulations discretized form. Then, apply nested Newton–Casulli–Zanolli (NCZ) algorithm one-dimensional finite-volume discretization energy–enthalpy formulation. Model performance demonstrated against Neumann Lunardini analytical solutions by comparing results experiments steps 1 h, d, 10 d. Using our NCZ solver With this approach, be chosen match timescale processes investigated.