Development of a Cell-Centred Finite Difference Numerical Methodology on Triangulated Domains
Bibliographic record
Abstract
A cell-centred finite difference (CCFD) method for unstructured mesh topology is proposed and applied to model partial differential equations (PDEs) governing fluid flow and solid mechanics phenomena. The numerical method implements a finite difference approximation at cell centroids by taking differencing points along orthogonal Cartesian axes localized within each cell. The predominant advantage of this method is that it can be applied to arbitrary mesh topologies, including structured, unstructured and hybrid meshes. Either a direct or iterative approach is used to solve the system of equations developed by the proposed method. The numerical method is designed to solve a variety of physical phenomena governed by PDEs, such as electrostatic potential in electromagnetic fields, stress and strain in structural mechanics and wave phenomena in physics. The focus of the thesis research is to investigate the application of this methodology in heat transfer and fluid mechanics problems. This new finite difference methodology is applied to typical "benchmark" problems in such fields, covering the representative in different types of PDEs with initial and boundary conditions. Solutions obtained are compared to exact solutions if available from analytical methods or to the results from other reliable numerical simulations.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".