Temperature-driven turbulence in compressible fluid flows

Bangwei She; Eduard Feireisl; Maria Lukacova-Medvidova; Yuhuan Yuan

arxiv: 2603.28158 · v2 · submitted 2026-03-30 · 🧮 math.NA · cs.NA

Temperature-driven turbulence in compressible fluid flows

Eduard Feireisl , Maria Lukacova-Medvidova , Bangwei She , Yuhuan Yuan This is my paper

Pith reviewed 2026-05-14 02:27 UTC · model grok-4.3

classification 🧮 math.NA cs.NA

keywords discretenumericalcompressibleflowsresultstemperature-drivenappliedattractor

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Numerical solutions via structure-preserving finite volume schemes for temperature-driven compressible flows generate discrete attractors that converge to continuous counterparts, with simulations indicating Gaussian invariant measures and persistent non-zero Reynolds stress.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Researchers examined how temperature differences drive motion in compressible fluids, such as air heated from below. They used a special numerical method that keeps key physical properties intact during calculations. The work shows that the long-term patterns captured by these computer simulations approach the mathematical ideal as the grid gets finer. In simulations of the classic Rayleigh-Benard setup, the system appears to visit all possible states over time as predicted by the ergodic hypothesis. The statistical descriptions of these long-term behaviors turn out to follow Gaussian distributions, which differs from an earlier conjecture. The calculations also suggest that turbulent momentum transfer, measured by Reynolds stress, remains active even after very long times rather than fading away.

Core claim

We show that numerical solutions of a structure-preserving finite volume method generate a discrete attractor that consists of entire discrete trajectories. Further, we prove the convergence of discrete attractors to their continuous counterparts. ... any invariant measure is of Gaussian type in sharp contrast with the conjecture proposed by [Glimm et al., SN Applied Sciences 2, 2160 (2020)].

Load-bearing premise

The finite volume method must preserve the required structure and the continuous compressible flow system must possess attractors for the convergence result to hold; these are invoked without detailed verification in the abstract.

read the original abstract

We study the long-time behaviour of the temperature-driven compressible flows. We show that numerical solutions of a structure-preserving finite volume method generate a discrete attractor that consists of entire discrete trajectories. Further, we prove the convergence of discrete attractors to their continuous counterparts. Theoretical results are illustrated by extensive numerical simulations of the well-known Rayleigh-Benard problem. The numerical results also indicate the validity of the ergodic hypothesis and imply that a non-zero Reynolds stress persist for long time. Finally, we also observe that any invariant measure is of Gaussian type in sharp contrast with the conjecture proposed by [Glimm et al., SN Applied Sciences 2, 2160 (2020)].

Editorial analysis

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Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard assumptions from PDE theory for compressible flows and the structure-preserving property of the chosen discretization; no free parameters or invented entities are indicated in the abstract.

axioms (2)

domain assumption The continuous temperature-driven compressible flow system possesses attractors to which discrete versions converge.
Invoked to establish the convergence result stated in the abstract.
domain assumption The finite volume method is structure-preserving.
Required for the discrete attractor to consist of entire trajectories.

pith-pipeline@v0.9.0 · 5414 in / 1284 out tokens · 57815 ms · 2026-05-14T02:27:09.820353+00:00 · methodology

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We show that numerical solutions of a structure-preserving finite volume method generate a discrete attractor that consists of entire discrete trajectories. Further, we prove the convergence of discrete attractors to their continuous counterparts.

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