A Free, Fast, Simple, and Efficient Total Variation Diminishing Magnetohydrodynamic Code
Bibliographic record
Abstract
We describe a numerical method to solve the magnetohydrodynamic (MHD) equations. The fluid variables are updated along each direction using the flux-conservative, second-order, total variation diminishing (TVD), upwind scheme of Jin & Xin. The magnetic field is updated separately in two-dimensional advection-constraint steps. The electromotive force (EMF) is computed in the advection step using the TVD scheme, and this same EMF is used immediately in the constraint step in order to preserve ∇ = 0 without the need to store intermediate fluxes. Operator splitting is used to extend the code to three dimensions, and Runge-Kutta is used to get second-order accuracy in time. The advantages of this code are high-resolution per grid cell, second-order accuracy in space and time, enforcement of the ∇ = 0 constraint to machine precision, no memory overhead, speed, and simplicity. A three-dimensional FORTRAN implementation less than 400 lines long is made freely available. We also implemented a fully scalable message-passing parallel MPI version. We present tests of the code on MHD waves and shocks.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.012 | 0.008 |
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".