A 3D MODEL FOR TWO COUPLED TURBULENT FLUIDS: NUMERICAL ANALYSIS OF A FINITE ELEMENT APPROXIMATION
Bibliographic record
Abstract
This paper deals with the numerical analysis for a finite element approximation of a steady coupled two-fluid RANS turbulence equations, used to model, for example, air-ocean flow interaction. Each fluid is modeled by the coupled steady Stokes equations with the equation for the turbulent kinetic energy TKE. The eddy viscosities for velocity and TKE depend on the energy. The production (source) term for the TKEs is only in L 1 , and the boundary condition for the TKEs on the interface between the two flows depends quadratically on the difference of velocities. To overcome the lack of regularity, we approximate the initial system by a regularized one, in which the eddy viscosities and source terms for the TKEs are regularized by convolution. We perform its finite element discretization, combined with a decoupled iterative lin-earization procedure. We prove that the discrete scheme converges to the continuous one for large enough eddy viscosities in natural norms. Finally, we present some numerical tests where we study the accuracy of the procedure, and simulate a realistic flow in which an imposed wind in the upper atmosphere generates an upwelling in the oceanic flow. 1. Introduction. We consider the numerical analysis for finite element approximation of RANS (Reynolds-Averaged Navier-Stokes) turbulence models, and more precisely of a coupled two-fluid RANS models. This system can model the coupled atmosphere-ocean system, whose accurate numerical simulation is crucial to analyze the main issues related to climate change. From the practical point of view, RANS models are rather diffusive and provide overall predictions of many flows of engineering interest (Cf. Davidson [21]). However, from the mathematical point of view RANS equations are more singular than the Navier-Stokes equations. The main mathematical difficulties comes from the source term (the production term) for the TKE equations which has a L 1 (Ω) regularity only, implying that the TKE equations do not make sense in H −1 (Ω). Their solution must be understood in the renormalized –or entropy– sense (Cf. [1, 7, 6, 8, 9, 10]).
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".