Flux-Based Alternative Formulation for Variably Saturated Subsurface Flow
Bibliographic record
Abstract
Finite-element and finite-difference solutions to different forms of the Richards equation can exhibit stability problems as well as mass balance errors. These problems are more pronounced for sharp wetting fronts in soils with very dry initial conditions and at material interfaces for layered soil profiles. The pressure head form can suffer from large mass balance errors while the moisture content form conserves mass perfectly but has difficulty handling material boundaries in layered soil profiles and near saturation conditions. This paper presents a conservative mixed formulation for the solution of the Richards equation of unsaturated flow by the finite-element method in which the discharge velocity (volumetric flux) and pressure head are the primary field variables. Solution techniques for various boundary conditions including prescribed constant pressure head and constant flux are also presented. The ability of the formulation to handle variably saturated domain and material heterogeneity is also established. Example solutions for infiltration into homogeneous and heterogeneous unsaturated and variably saturated soil profiles are compared with finite-element and finite-difference solutions of pressure head and mixed form of Richards equation. Results indicate that the alternative formulation is mass conservative, stable, and can better handle heterogeneous boundaries and variably saturated flow domains.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".