A spectral approach to inertial confined thin‐film flow
Bibliographic record
Abstract
SUMMARY A spectral approach is proposed to determine the flow field of a thin film inside narrow channels of arbitrary shape. Although the method is easily extended to transient flow, only steady flow is considered here. The flow field is represented spectrally in the depthwise direction in terms of orthonormal shape functions, which together with the Galerkin projection lead to a system of ordinary differential equations that can be solved using standard methods. The method is particularly effective for nonlinear flow, including nonlinearities of geometrical or material origins. The validity of the proposed method is demonstrated for a flow with inertia, and, unlike the depth‐averaging method, is not limited to a flow at small Reynolds number. The problem is closely related to high‐speed lubrication flow. The validity of the spectral representation is assessed by examining the convergence of the method, and comparing it with the fully two‐dimensional finite‐element solution, and the widely used depth‐averaging method from shallow‐water theory. It is found that a low number of modes are usually sufficient to secure convergence and accuracy. The influence of inertia is examined on the velocity and pressure fields. The pressure distributions reflect excellent agreement between the low‐order spectral method and the finite‐element solution, even at moderately high Reynolds number. The depth‐averaging solution is unable to predict accurately (qualitatively and quantitatively) the high‐inertia flow. Comparison of the velocity field reflects the expected discrepancy in a boundary layer formulation. Copyright © 2012 John Wiley & Sons, Ltd.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".