Abstract
Abstract. Phenomena involving frozen soil or rock are important in many natural systems and, as a consequence, there is a great interest in the modeling of their behavior. Few models exist that describe this process for both saturated and unsaturated soil and in conditions of freezing and thawing, as the energy equation shows strongly non-linear characteristics and is often difficult to handle with normal methods of iterative integration. Therefore in this paper we propose a method for solving the energy equation in freezing soil. The solver is linked with the solution of Richards equation, and is able to approximate water movement in unsaturated soils and near the liquid-solid phase transition. A globally-convergent Newton method has been implemented to achieve robust convergence of this scheme. The method is tested by comparison with an analytical solution to the Stefan problem and by comparison with experimental data derived from the literature.
Highlights
The analysis of freezing/thawing processes and phenomena in the ground is important for hydrological and other land surface and climate model simulations (e.g. Viterbo et al, 1999; Smirnova et al, 2000)
Numerical physicallybased algorithms simulate ground freezing by numerically solving the complete energy equation, and in natural conditions they are expected to provide the best accuracy in simulating ground thawing and freezing (Zhang et al, 2008)
This approach has difficulties, especially regarding the treatment of phase change, which is strongest in a narrow range of temperatures near the melting point, and represents a discontinuity that may create numerical oscillations (Hansson et al, 2004)
Summary
The objectives of the paper are: (1) to revisit the theory of the freezing soil in order to provide the formulation for the unfrozen water pressure, which can accomodate variablysaturated soils; (2) to outline and describe a numerical approach for solving coupled mass and energy balance equations in variably-saturated freezing soils, based on the splitting method; (3) to provide an improved numerical scheme that: (i) is written in conservative way, (ii) is based on the globally convergent Newton scheme, and (iii) can handle the high non-linearities typical of the freezing/thawing processes. The algorithm is tested against the analytical solution of unilateral freezing of a semi-infinite region given by Neumann (Carslaw and Jaeger, 1959; Nakano and Brown, 1971), in order to test convergence under extreme conditions, and against the experimental results published by Hansson et al (2004), in order to test the coupled water and heat flow
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