A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation
Bibliographic record
Abstract
Abstract. The accurate simulation of heat transfer with phase change is a central problem in cryosphere studies. This is because the nonlinear behaviour of enthalpy as function of temperature can prevent thermal models of snow, ice and frozen soil from converging to the correct solution. Existing numerical techniques rely on increased temporal resolution in trying to keep corresponding errors withing acceptable bounds. Here, we propose an algorithm, originally applied to solve water flow in soils, as a method to solve these integration issues with guaranteed convergence and conservation of energy for any time step size. We review common modeling approaches, focusing on the fixed-grid method and on frozen soil. Based on this, we develop a conservative formulation of the governing equation and outline problems of alternative formulations in discretized form. Then, we apply the nested Newton-Casulli-Zanolli (NCZ) algorithm to a one-dimensional finite-volume discretization of the energy-enthalpy formulation. Model performance is demonstrated against the Neumann and Lunardini analytical solutions and by comparing results from numerical experiments with integration time steps of one hour, one day, and ten days. Using our formulation and the NCZ algorithm, the convergence of the solver is guaranteed for any time step size. With this approach, the integration time step can be chosen to match the time scale of the processes investigated.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".