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arXiv · 2605.23380

Lowest order Carleman linearization for low Reynolds long-term behaviour of fluid flow simulations

Luca Cappelli·Sauro Succi
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Abstract

It is shown that the lowest (second) order truncation of the Carleman linearization of the fluid equations (C2) recovers the late stage of the evolution, namely the steady-state solution, although to a decreasing degree of accuracy at increasing Reynolds number. This asymptotic property is first proved analytically for the decaying logistic with external forcing and then shown to hold to a significant degree of accuracy also for the more complex case of two-dimensional Kolmogorov-like fluid flow at low Reynolds numbers, below $Re \sim 10$. This time-asymptotic property may open interesting prospects for the quantum simulation of low-Reynolds steady-state fluid flows.

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Luca Cappelli, Sauro Succi. 2026-06-10. Lowest order Carleman linearization for low Reynolds long-term behaviour of fluid flow simulations. https://arxiv.org/abs/2605.23380

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