Implicit Subtime Stepping for Solving Nonlinear Flow Equations in an Integrated Surface–Subsurface System
Bibliographic record
Abstract
A diverse group of problems requires quantification of the entire hydrologic cycle by the integrated simulation of water flow in the surface and subsurface regimes. In a transient integrated simulation of the water cycle, the time step size is a key factor in controlling the solution accuracy and the simulation efficiency for a given spatial discretization. In general, if the time step size is sufficiently small, the resulting solution becomes more accurate but with higher computational cost. Thus, to maintain an acceptable level of solution accuracy in the entire simulation domain, the time step size is restricted by the relatively rapid responses in the surface flow regime. As the relatively rapid responses are typically limited to a small portion of the surface domain compared with the groundwater system, a large portion of the domain tends to be temporally overdiscretized. The implicit subtime stepping approach described here can apply smaller subtime steps only to the subdomain where the accuracy requirements are needed. In this work, generalized formulations for implicit subtime stepping in the numerical solution of the nonlinear coupled surface–subsurface equations were derived and implemented into the integrated model HydroGeoSphere. Application to several problems showed that implicit subtime stepping can significantly improve the simulation efficiency with minimal loss in accuracy. The methodology was successfully applied to enhance the computational efficiency of an integrated flow simulation in the San Joaquin Valley, California, where the characteristic response time near surface drainage streams is orders of magnitude shorter than in the groundwater regime.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".