A Hybrid, Explicit-Implicit, Second Order in Space and Time TVD scheme for One-Dimensional Scalar Conservation Laws
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Bibliographic record
Abstract
A hybrid, explicit-implicit, method for hyperbolic conservation laws is proposed. The scheme is of the second order both in space and in time for both, explicit and implicit, modes on smooth solutions. In order to satisfy the Total Variation Diminishing (TVD) property and obtain monotone solutions in the presence of discontinuities, TVD limiters are applied to both spatial and temporal gradients of solution. The Lower-Upper-Symmetric-GaussSeidel (LU-SGS) approximate factorization method is used to solve the discretized and linearized governing equations. Iterations are performed at each time step to eliminate the factorization and linearization errors. The numerical results for the linear advection equation and the Burgers equation demonstrate the performance of the proposed scheme in comparison with other existing hybrid methods.
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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.
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