A hybrid, explicit-implicit, second-order TVD method on adaptive unstructured grids for unsteady compressible flows
Bibliographic record
Abstract
This work is devoted to the development of a hybrid, explicit-implicit, scheme for simulation of unsteady compressible flows with shock waves.The proposed scheme is of the second-order accuracy in space and time for both explicit and implicit modes, while satisfying the TVD (Total Variation Diminishing) property.The scheme is designed for simulation of the compressible flows with temporal stiffness.In this situation, the numerical time step of explicit schemes is severely limited by particular conditions in a relatively small part of the computational domain, while the rest of the domain admits much higher time steps.The hybrid scheme is designed to operate in its implicit mode in the small areas causing temporal stiffness, thus allowing to proceed with higher time steps and reduce the computational time.In this study, a new hybridization approach is suggested.On its basis, the hybrid scheme is first introduced for hyperbolic conservation laws in one dimension.In order to satisfy the TVD property and obtain monotone solutions in the presence of discontinuities, TVD limiters are applied to both spatial and temporal reconstructions.The second-order accuracy in time for the implicit mode, which is the main distinction of the proposed hybrid scheme in comparison with the existing methods, is achieved through a reconstruction of the solution in time.To make the reconstruction TVD preserving, a novel time limiter is derived.The stability condition and the relation to the hybridization factor of the new scheme are obtained.Moreover, the relationship of the proposed scheme with another existing hybrid method is revealed and analyzed.A set of one-dimensional test problems is used to demonstrate the 4-28 Mach number contours of shock tunnel.Scales are different in x and y directions. . . . . . . . . . . .
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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) | 0.001 | 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 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".