A parallel hp-adaptive high order discontinuous Galerkin method for the incompressible Navier-Stokes equations
Bibliographic record
Abstract
We present a parallel hp-adaptive high order (spectral) discontinuous Galerkin method for approximation of the incompressible Navier-Stokes equations. The spatial discretization consists of equal-order polynomial approximations of the fluid velocity and pressure via discontinuous Galerkin spatial discretizations. For the nonlinear convective term we select the local Lax-Friedrichs flux, while for the divergence and gradient operators central fluxes are chosen. For the diffusive term, we use an interior penalty discontinuous Galerkin method to ensure stability and invertibility. The temporal discretization is an implicit-explicit Runge-Kutta method paired with a high-order splitting procedure to efficiently enforce the incompressibility condition at each time step. The compact stencil size, explicit time stepping of nonlinear terms, and inversion of sparse linear systems make the resulting method simple to parallelize while the local nature of the discontinuous Galerkin approximation makes hp-adaptive refinement natural to implement. We detail our implementation consisting of a tensor product basis of high order polynomials on quadrilateral elements, and implement hp-adaptivity using an inexpensive a posteriori error estimator to determine where refinement is necessary. p-Multigrid and pressure projection techniques are used to precondition the conjugate gradient linear solvers. We present several numerical tests to demonstrate the efficacy of the method, in particular in reducing the number of degrees of freedom needed and allocating computing resources to regions of sharp variation in transient incompressible Navier-Stokes flows.
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 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) | 0.000 | 0.000 |
| 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) | 0.003 | 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".