A hybrid differencing scheme for mass transport in electrochemical systems
Bibliographic record
Abstract
Purpose To present a new hybrid differencing scheme for the numerical solution of an electromigration‐diffusion equation. The value of this work is evidenced by demonstrated improvement in the simulation of the Fu and Chan experiment when using the hybrid scheme. Design/methodology/approach A hybrid differencing scheme is developed which is based upon the solution of the pseudo‐steady state electromigration‐diffusion equation. In this scheme, a weighting parameter is calculated that varies the relative influence of the upwind node (relative to the direction of electromigration). This scheme significantly enhances the accuracy of electrochemical system mass transport models. Findings The hybrid scheme was compared to the upwind scheme. Use of the new hybrid scheme improved the accuracy of the model predictions by as much as 87 percent compared to the upwind scheme. However, use of the new scheme also increased the simulation time by between 6 and 43 percent. Deviations from electroneutrality and the presence of an activity coefficient gradient were detrimental to the stability of the hybrid scheme. Research limitations/implications This scheme is presented in the paper as an one‐dimensional (1D) scheme. However, it could be extended to more than 1D but some artificial viscosity may result. Practical implications The hybrid scheme developed and demonstrated herein is useful for researchers developing mass transport models of electrochemical systems. It has been proven capable of improving the accuracy of electrolyte mass transport models. Originality/value This is the first hybrid differencing scheme designed for the special characteristics of electrochemical mass transport systems. It greatly improves the accuracy of simulation results. This work is useful to those who mathematically model electrochemical systems.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".