Parallel Implicit Adaptive Mesh Refinement Scheme for Body-Fitted Multi-Block Mesh
Bibliographic record
Abstract
A parallel implicit adaptive mesh refinement (AMR) algorithm is described for the system of partial-differential equations governing steady two-dimensional compressible gaseous flows. The AMR algorithm uses an upwind finite-volume spatial discretization procedure in conjunction with limited linear solution reconstruction and Riemann-solver based flux functions to solve the governing equations on multi-block mesh composed of structured curvilinear blocks with quadrilateral computational cells. A flexible block-based hierarchical data structure is used to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. A matrix-free inexact Newton method is used to solve the system of nonlinear equations arising from this finite-volume spatial discretization procedure and a preconditioned generalized minimal residual (GMRES) method is used to solve the resulting non-symmetric system of linear equations at each step of the Newton algorithm. Right preconditioning of the linear system is used to improve performance of the Krylov subspace method. An additive Schwarz global preconditioner with variable overlap is used in conjunction with block-fill incomplete lower-upper (BFILU) type preconditioners based on the Jacobian of the first-order upwind scheme for each sub-domain. The Schwarz preconditioning and block-based data structure readily allow efficient and scalable parallel implementations of the implicit AMR approach on distributed-memory multi-processor architectures. Numerical results are described for several flow cases, demonstrating both the effectiveness of the mesh adaptation and algorithm parallel performance. The proposed parallel implicit AMR method allows for anisotropic mesh refinement and appears to be well suited for predicting complex flows with disparate spatial and temporal scales in a reliable and efficient fashion. I.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".