Numerical simulation of Neumann boundary condition in the thermal lattice Boltzmann model
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Bibliographic record
Abstract
In this paper, a bilinear interpolation finite-difference scheme is proposed to handle the Neumann boundary condition with nonequilibrium extrapolation method in the thermal lattice Boltzmann model. The temperature value at the boundary point is obtained by the finite-difference approximation, and then used to determine the wall temperature via an extrapolation. Our method can deal with the boundaries with complex geometries, motions and gradient boundary conditions. Several simulations are performed to examine the capacity of this proposed boundary method. The numerical results agree well with the analytical solutions. When compared with a representative boundary method, an improved performance is observed. The results also show that the proposed scheme together with nonequilibrium extrapolation method has second-order accuracy.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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.
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