Accelerated implicit-explicit Runge-Kutta schemes for locally stiff systems
Bibliographic record
Abstract
In this paper we introduce a family of accelerated implicit-explicit (AIMEX) schemes for the solution of stiff systems of equations. Similar to conventional IMEX schemes, AIMEX schemes allow a problem to be split into its stiff and non-stiff constituent parts. These are then advanced in time using an implicit and explicit scheme, respectively. By design, AIMEX schemes have an arbitrarily large number of stages. This allows for optimization of the explicit part to improve its stability properties, increasing the allowable time step size. Importantly, only two implicit stages are required regardless of the total number of stages, meaning a larger global time step can be taken with significantly fewer implicit stages for a given simulation time. Numerical results demonstrate that AIMEX schemes achieve their designed order of accuracy for linear and non-linear problems involving mesh induced stiffness. Simulations of unsteady flow over an SD7003 airfoil using the compressible Navier-Stokes equations demonstrate that AIMEX schemes can significantly outperform classical explicit Runge-Kutta schemes by over a factor of 20, and conventional IMEX schemes by over a factor of two, with negligible impact on quantitative results. Finally, a demonstration case of Implicit Large Eddy Simulation (ILES) of flow over a stalled NACA0020 airfoil shows the utility of AIMEX schemes for wall-bounded turbulent flows.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".