Efficient solution-adaptive finite-volume scheme for time-invariantmulti-dimensional solutions of maximum-entropy-based 14-moment closure fornon-equilibrium gases
Bibliographic record
Abstract
A computationally efficient solution-adaptive finitevolume scheme is proposed and developed for obtaining timeinvariant multi-dimensional solutions of a novel maximum-entropybased, interpolative, 14-moment closure which provides a fully hyperbolic description of non-equilibrium transport phenomena in monatomic gases, including heat transfer. Unlike the maximumentropy closure on which it is based, the interpolative closure provides approximate closed-form expressions for the closing fluxes. A Godunov-type finite-volume with piecewise limited linear solution reconstruction is combined with an adaptive mesh refinement (AMR) algorithm permitting local refinement to obtain solutions to the governing hyperbolic system of moment equations on twodimensional, body-fitted, multi-block grids consisting of quadrilateral cells. Time-invariant solutions of the spatially-discretized moment equations are obtained by using an inexact Newton’s method combined with a preconditioned Krylov subspace iterative method. In particular, the GMRES (Generalized Minimal RESidual) iterative method is combined with a Schwarz-type preconditioning strategy based on the multi-block grid in the iterative solution solution of linear equations at each Newton step. The application of the 14moment closure is considered for some canonical non-equilibrium flow problems, including subsonic flow around a circular-cylinder and a lid driven cavity flow. The predictive capabilities of the 14-moment interpolative closure are shown to surpass those of the regularized Gaussian closure, which models heat transfer through the addition of elliptic terms using a regularization technique applied to the low-order Gaussian closure. The 14-moment closure is also found to predict interesting non-equilibrium phenomena, such as counter-gradient heat transfer, a highly non-equilibrium phenomenon.
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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) | 0.000 | 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 | 0.000 |
| 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".