A FOURTH-ORDER ACCURATE SCHEME FOR SOLVING ONE-DIMENSIONAL HIGHLY NONLINEAR STANDING WAVE EQUATION IN DIFFERENT THERMOVISCOUS FLUIDS
Bibliographic record
Abstract
Combination of a fourth-order Padé compact finite difference discretization in space and a fourth-order Runge–Kutta time stepping scheme is shown to yield an effective method for solving highly nonlinear standing waves in a thermoviscous medium. This accurate and fast-solver numerical scheme can predict the pressure, particle velocity, and density along the standing wave resonator filled with a thermoviscous fluid from linear to strongly nonlinear levels of the excitation amplitude. The stability analysis is performed to determine the stability region of the scheme. Beside the fourth-order accuracy in both time and space, another advantage of the given numerical scheme is that no additional attenuation is required to get numerical stability. As it is well known, the results show that the pressure and particle velocity waveforms for highly nonlinear waves are significantly different from that of the linear waves, in both time and space. For highly nonlinear waves, the results also indicate the presence of a wavefront that travels along the resonator with very high pressure and velocity gradients. Two gases, air and CO 2, are considered. It is observed that the slopes of the traveling velocity and pressure gradients are higher for CO 2 than those for air. For highly nonlinear waves, the results also indicate the higher asymmetry in pressure for CO 2 than that for air.
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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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".