Axially symmetric pseudo-Newtonian hydrodynamics code
Bibliographic record
Abstract
We develop a numerical hydrodynamics code using a pseudo-Newtonian formulation that uses the weak-field approximation for the geometry, and a generalized source term for the Poisson equation that takes into account relativistic effects. The code was designed to treat moderately relativistic systems such as rapidly rotating neutron stars. The hydrodynamic equations are solved using a finite volume method with high-resolution shock-capturing techniques. We implement several different slope limiters for second-order reconstruction schemes and also investigate higher order reconstructions such as the piecewise parabolic method, essentially non-oscillatory method (ENO) and weighted ENO. We use the method of lines to convert the mixed spatial-time partial differential equations into ordinary differential equations (ODEs) that depend only on time. These ODEs are solved using second- and third-order Runge-Kutta methods. The Poisson equation for the gravitational potential is solved with a multigrid method, and to simplify the boundary condition, we use compactified coordinates which map spatial infinity to a finite computational coordinate using a tangent function. In order to confirm the validity of our code, we carry out four different tests including one- and two-dimensional shock tube tests, stationary star tests of both non-rotating and rotating models, and radial oscillation mode tests for spherical stars. In the shock tube tests, the code shows good agreement with analytic solutions which include shocks, rarefaction waves and contact discontinuities. The code is found to be stable and accurate: for example, when solving a stationary stellar model the fractional changes in the maximum density, total mass, and total angular momentum per dynamical time are found to be 3 × 10−6, 5 × 10−7 and 2 × 10−6, respectively. We also find that the frequencies of the radial modes obtained by the numerical simulation of the steady-state star agree very well with those obtained by linear analysis.
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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 | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.013 | 0.004 |
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".