The Natural Element Methods and its Applications in Solid and Fluid Mechanics
Bibliographic record
Abstract
The natural element method (NEM) has been successfully used to simulate several problems in solid mechanics and has shown a big potential. As an example, we mention the simulation of metal cutting and the behaviour of the human menisci. It was also used in fluid mechanics in an updated-Lagrangian formulation for the mould filling simulation [1]. The NEM, in its two interpolation manners (Sibson and Laplace) give the same advantages as the finite element method such as nodal interpolation, the partition of unity, the linear completeness. In addition, its interpolation shape function could be taken as a finite volume one where the fluxes are computed on Voronoï edges.In this talk, we will begin by presenting briefly the natural element method with its two versions. We will illustrate some applications in solid mechanics achieved in the LMSP (ENSAM Paris). Then, we will focus on its applications in fluid mechanics and especially in hydraulics. A fully Lagrangian finite volume method inspired from the NEM is applied to simulate inviscid shallow water flows. The shallow-water equations are used to achieve such aim. Solving these equations present numerical challenges such as the stability issue, discontinuous solutions and the presence of shock waves. Besides, standard methods (finite elements and finite volumes methods) have shown difficulties to handle shallow water flows especially for simulating the wet-dry phenomenon.After a presentation of St-Venant equations written in the framework of the new NEM formulation, stabilization issue is tackled. The shock capturing is improved by upwinding the schema using an artificial viscosity [2]. Some examples of flows in 2D and pseudo 3D prismatic channels are used as benchmarks. This work represents a first step in applying the NEM in hydraulics. The introduction of source terms, a variable bathymetry and complex geometry with moving boundaries represent following steps to explore in the future.
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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 | 0.002 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.003 |
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".