Upscaling permeability to unstructured grids using the multipoint flux approximation
Bibliographic record
Abstract
Grids used for flow simulation are often at a much coarser scale than that of grids for geological modelling due to computational demand. Unstructured grids offer increased flexibility for the flow grid design; however, solving the flow equations and upscaling from high resolution geological grids to the coarse flow grid is more complex than using coarse regular grids. The multipoint flux approximation (MPFA) is one technique applied to discretize the flow equations on unstructured grids. This paper develops an upscaling technique that uses the MPFA method to solve the flow equations on the fine- and coarse-scale grids. Unlike most cases where the fine-scale grid is regular or structured, this work utilizes a high resolution triangular grid that conforms to the coarse-scale grid. The triangular grid is generated using the coarse-scale interaction regions as constraints. Upscaling leads to transmissibility matrices of the coarse-scale interaction regions. Two different types of local boundary conditions for the MPFA upscaling approach are developed, including linear varying pressures and pressures computed by solving the flow equations around the element boundary. The method is tested using flow simulation on several cases. Results are comparable with flow using a high resolution regular grid.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 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".