A novel velocity discretization for lattice Boltzmann method: Application to compressible flow
Bibliographic record
Abstract
The lattice Boltzmann method (LBM) has emerged as a powerful tool in computational fluid dynamics and materials science. However, due to the failure to accurately reproduce the third moment of the equilibrium distribution function, the standard LBM formulation does not recover the correct compressible Navier–Stokes equations at macroscale. It only recovers Navier–Stokes in the incompressible limit. The errors include terms that destroy Galilean invariance in the presence of density variations. In this paper, we introduce a new velocity discretization method to overcome some of these challenges. In this new formulation, the particle populations are discretized using a bump function that has a mean and a variance. This introduces enough independent degrees of freedom to set the equilibrium moments to the moments of Maxwell–Boltzmann distribution up to and including the third moments. Consequently, the correct macroscopic fluid dynamics equations for compressible fluids are recovered. This new method does neither require introducing ad hoc correction terms or coupling to an extra potential nor significantly alter the implementation. As a result, it is not considerably more complicated or computationally heavy compared to the original LBM but provides a significantly improved hydrodynamics. We validate our method using several benchmark simulations of isothermal compressible flows, including Poiseuille flow, sound wave decay, Couette flow in the presence of a density gradient, and flow over a cylinder. We show that the new formulation restores Galilean Invariance, by comparison to analytical solutions (less than 0.1% mean error), and is capable of capturing flows with large density variations, high Reynolds numbers (∼1000), and Mach numbers near 1.
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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 | 0.000 |
| 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".