High order mimetic difference simulation of unsaturated flow using Richards equation
Bibliographic record
Abstract
The vadose zone is the portion of the subsurface above the water table and its pore space usually contains air and water. Due to the presence of infiltration, erosion, plant growth, microbiota, contaminant transport, aquifer recharge, and discharge to surface water, it is crucial to predict the transport rate of water and other substances within this zone. However, flow in the vadose zone has many complications as the parameters that control it are extremely sensitive to the saturation of the media, leading to a nonlinear problem. This flow is referred as unsaturated flow and is governed by Richards equation. Analytical solutions for this equation exists only for simplified cases, so most practical situations require a numerical solution. Nevertheless, the nonlinear nature of Richards equation introduces challenges that causes numerical solutions for this problem to be computationally expensive and, in some cases, unreliable. High order mimetic finite difference operators are discrete analogs of the continuous differential operators and have been extensively used in the fields of fluid and solid mechanics. In this work, we present a numerical approach involving high order mimetic operators along with a Newton root-finding algorithm for the treatment of the nonlinear component. Fully-implicit time discretization scheme is used to deal with the problem’s stiffness.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 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".