A 2D Moving Mesh Finite Element Analysis of Heat Transfer in Arctic Soils

Abstract

Accurate soil heat transfer models are needed to predict and adapt to a warming arctic. A numerical model to accurately predict temperatures and thaw depths in soils, both with depth and with horizontal distance from features such as cliffs, was developed in Matlab using the finite element method. The model was validated against analytical solutions to simple versions of the problem and experimental temperature data from borehole thermistor strings on the north shore of Alaska. The current model is most useful for short term (on the order of days) predictions of thaw depth and near surface temperatures in homogeneous soils with existing data to allow the calibration of soil thermal parameters. These are exactly the time scales and capabilities that would integrate well with erosional models to predict the erosion during storm events and summer thaw conditions. Comparisons with analytical solutions show the model to be fairly accurate in predictions of temperatures thaw-depth and temperatures, within about 0.25 °C and 0.02 m respectively, for reasonable arctic soil parameters. Differences between predicted temperatures and thaw-depth against borehole data from Barter Island, Alaska are within about 1 °C and 0.5 m respectively. Comparison to commercial software, which does not directly track and move the phase change boundary, shows that this moving-mesh model has much better agreement. The model developed in this work is flexible and can be modified to model a wide variety of problems, but is efficiently set up to take a surface and thaw-boundary profile (not necessarily horizontal) and use soil parameters and surface boundary conditions appropriate to Arctic regions. It has been verified to appropriately model cliffs, which are particularly vulnerable to erosion.

Keywords

• permafrost
• finite element
• finite difference
• moving mesh
• Arctic soil
• thawing