An Analytic Element Method solution for multispecies reactive contaminant transport
Bibliographic record
Abstract
A new analytic element approach is presented for steady-state reactive contaminant transport modelling with circular boundaries. Two solute compounds (electron donor and electron acceptor) are assumed to undergo an instantaneous and binary reaction [1] in a uniform flow field, forming a steady plume [2]. Transformations of the advection-dispersion-reaction equation are applied resulting in a reactive contaminant transport system governed by the modified Helmholtz equation. Comprehensive solutions to a single as well as multiple superimposed, interacting circular contaminant (electron donor) source elements are expressed by infinite series expansions of Mathieu functions [3]. The concentration of the electron donor and electron acceptor can be calculated at any point in the domain, while boundary conditions are met approximately, by adjusting the unknown coefficients of the truncated series of Mathieu functions. Accuracy at the boundary interfaces is increased with an increase of number of terms used in the Mathieu functions series expansion. The potential of this novel approach lies in the flexibility of boundary conditions, while maintaining computational efficiency.The model is implemented using the Python programming language. Model verification was achieved by evaluating the residual of a central difference scheme, evaluation of the error along the boundary interfaces and a comparison with a simple MODFLOW / MT3DMS model setup. Current development includes expansion of the model to line source elements and discontinuous contaminant sources. Further advancements may be achieved by increasing source shape complexity of contaminant sources by superimposing a large number of elements and introducing remediation actions in the form of interacting electron acceptor elements.[1] O. A. Cirpka, Å. Olsson, Q. Ju, Md. A. Rahman, and P. Grathwohl, ‘Determination of Transverse Dispersion Coefficients from Reactive Plume Lengths’, Groundwater, vol. 44, no. 2, pp. 212–221, 2006, doi: 10.1111/j.1745-6584.2005.00124.x.[2] R. Liedl, A. J. Valocchi, P. Dietrich, and P. Grathwohl, ‘Finiteness of steady state plumes’, Water Resources Research, vol. 41, Dec. 2005, doi: 10.1029/2005WR004000.[3] M. Bakker, ‘Modeling groundwater flow to elliptical lakes and through multi-aquifer elliptical inhomogeneities’, Advances in Water Resources, vol. 27, no. 5, pp. 497–506, May 2004, doi: 10.1016/j.advwatres.2004.02.015.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".