An Optimally Stable and Accurate Second‐Order SSP Runge‐Kutta IMEX Scheme for Atmospheric Applications
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Bibliographic record
Abstract
Abstract The objective of this paper is to develop an optimized implicit‐explicit (IMEX) Runge‐Kutta scheme for atmospheric applications focusing on stability and accuracy. Following the common terminology, the proposed method is called IMEX‐SSP2(2,3,2), as it has second‐order accuracy and is composed of diagonally implicit two‐stage and explicit three‐stage parts. This scheme enjoys the Strong Stability Preserving (SSP) property for both parts. This new scheme is applied to nonhydrostatic compressible Boussinesq equations in two different arrangements, including (i) semiimplicit and (ii) Horizontally Explicit‐Vertically Implicit (HEVI) forms. The new scheme preserves the SSP property for larger regions of absolute monotonicity compared to the well‐studied scheme in the same class. In addition, numerical tests confirm that the IMEX‐SSP2(2,3,2) improves the maximum stable time step as well as the level of accuracy and computational cost compared to other schemes in the same class. It is demonstrated that the A‐stability property as well as satisfying “second‐stage order” and stiffly accurate conditions lead the proposed scheme to better performance than existing schemes for the applications examined herein.
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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 | 0.001 |
| 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