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 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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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".