A Fourth-Order Compact Finite Difference Scheme for Solving Unsteady Convection-Diffusion Equations
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Bibliographic record
Abstract
Convection-diffusion equations are widely used for modeling and simulations of various complex phenomena in science and engineering Since for most application problems it is impossible to solve convection-diffusion equations analytically, efficient numerical algorithms are becoming increasingly important to numerical simulations involving convection-diffusion equations. Recently a great deal of efforts have been devoted to developing high-order compact schemes, which utilize only the grid nodes directly adjacent to the central node. In This method is very stable and accurate (third-order in space and second-order in time). In The scheme is defined on a single square cell of size 2x over a nine-point stencil. In In This method was further extended by In This new method is second-order in time and fourth-order in space, and is computationally efficient. In (Tian & Dai, 2007), Tian and Dai proposed a class of high-order compact exponential finite difference methods for solving one-and two-dimensional steady-state convection-diffusion problems. This method is nonoscillatory, fourth-order in space, and easy to implement. Some more recent high-order ADI methods for unsteady convection-diffusion equations can be found in
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| 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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it