The Meshfree Interface Finite Element Method for Numerical Simulation of Dendritic Solidification with Fluid Flow
Bibliographic record
Abstract
In this paper, we use the newly proposed meshfree interface finite element method (MIFEM) for numerical simulation of dendritic solidification with fluid flow. In the MIFEM, meshfree points without connectivity are imposed directly at the zero-isocontour of an implicit function defining the interface which is allowed to arbitrarily intersect the finite elements. The MIFEM utilizes the constructed interface points for meshfree solution of a variational level set equation based on the Ginzburg–Landau energy functional minimization such that the reinitialization procedure is completely eliminated. To account for inter-element discontinuities, field variables at interface-embedded elements are computed by extending the approximation using the meshfree interface points as additional degrees of freedom directly corresponding to the interface. This is achieved by meshfree interpolation at the interface region via radial basis functions which inherently satisfies the Kronecker-delta and the partition of unity conditions allowing for precise and easy imposition of Dirichlet boundary conditions at the interface. We use the MIFEM for solving the interfacial evolution equation and the set of mass, momentum, and energy conservation equations describing the dendritic solidification process with fluid flow. Mathematical formulation and implementation to multiple case studies will be presented and discussed.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".