The Compressible euler system and its numerical analysis
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Bibliographic record
Abstract
In this thesis we analyze the compressible Euler equations in one and two dimensions. For this purpose, we firstly consider a particular form of this system, namely the inviscid Burgers equation, which can be derived by imposing vanishing pressure to the Euler system. The inviscid Burgers equation leads us to understand the idea behind discontinuous solutions such as shock and rarefaction waves. A brief analysis of smooth and weak solutions with necessary conditions for choosing physically meaningful solutions among the others, entropy and Rankine-Hugonoit conditions are studied in the first part of this work. In the second part, the derivation of the compressible Euler equations is demonstrated in one dimension where the thermodynamic aspects are given to understand the nature of the Euler system. Furthermore, in order to illustrate the model numerically, the stability analysis of three different methods, namely Lax Friedrich, two step Lax Wendroff, and two step MacCormack methods, are examined in one dimensional case. We use Sod shock tube problem to test numerical methods since analytic solution of this problem exists. We finalize this work by a particular illustration of the Euler model in two dimensional case by applying the Lax Friedrich’s method with a short concluding remark.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it