Quantum-Inspired Simulation of 2D Turbulent Rayleigh-Bénard Convection

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: van Hülst, Nis-Luca, Cecile, Mario Guillaume, Van, Hai-Yen, Hashizume, Tomohiro, de Villiers, Eugene, Jaksch, Dieter
Format: Preprint
Veröffentlicht: 2026
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866915942250840064
author van Hülst, Nis-Luca
Cecile, Mario Guillaume
Van, Hai-Yen
Hashizume, Tomohiro
de Villiers, Eugene
Jaksch, Dieter
author_facet van Hülst, Nis-Luca
Cecile, Mario Guillaume
Van, Hai-Yen
Hashizume, Tomohiro
de Villiers, Eugene
Jaksch, Dieter
contents Turbulent thermal convection governs heat transport in systems ranging from stellar interiors to industrial heat exchangers. Two-dimensional Rayleigh-Bénard convection serves as a paradigm for these flows, reproducing key features such as thin boundary layers, large-scale circulation, and sustained plume dynamics. While Matrix Product State (MPS) methods have demonstrated significant compression of isothermal turbulent fields, their application to buoyancy-driven flows with active thermal coupling has remained unexplored. We apply MPS to two-dimensional Rayleigh-Bénard convection with dynamical simulations up to $\mathrm{Ra} = 10^{10}$. An a priori decomposition of DNS snapshots up to $\mathrm{Ra} = 10^{11}$ shows that the bond dimension $χ$ required to represent the flow fields grows without saturation, in contrast to the plateauing of $χ$ reported for velocity fields in isothermal 2D turbulence. Crucially, however, dynamical simulations solving the governing equations directly in the compressed MPS format at fixed $χ$ show that the $χ$ required to recover statistical observables, such as the Nusselt number, scales significantly more favorably with $\mathrm{Ra}$ than the a priori complexity suggests. At $\mathrm{Ra} = 10^{10}$, a relative error of $1.8\%$ in the mean Nusselt number is achieved with a nearly 9-fold reduction in degrees of freedom, using a $χ$ comparable to that required at $\mathrm{Ra} = 10^{9}$. Spectral analysis confirms the progressive recovery of spatial and temporal scales with increasing $χ$. These findings establish MPS as a scalable tool for simulating thermally driven turbulence, suggesting the method may remain viable for investigations of the ultimate regime at substantially higher $\mathrm{Ra}$.
format Preprint
id arxiv_https___arxiv_org_abs_2604_16179
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Quantum-Inspired Simulation of 2D Turbulent Rayleigh-Bénard Convection
van Hülst, Nis-Luca
Cecile, Mario Guillaume
Van, Hai-Yen
Hashizume, Tomohiro
de Villiers, Eugene
Jaksch, Dieter
Fluid Dynamics
Computational Physics
Quantum Physics
Turbulent thermal convection governs heat transport in systems ranging from stellar interiors to industrial heat exchangers. Two-dimensional Rayleigh-Bénard convection serves as a paradigm for these flows, reproducing key features such as thin boundary layers, large-scale circulation, and sustained plume dynamics. While Matrix Product State (MPS) methods have demonstrated significant compression of isothermal turbulent fields, their application to buoyancy-driven flows with active thermal coupling has remained unexplored. We apply MPS to two-dimensional Rayleigh-Bénard convection with dynamical simulations up to $\mathrm{Ra} = 10^{10}$. An a priori decomposition of DNS snapshots up to $\mathrm{Ra} = 10^{11}$ shows that the bond dimension $χ$ required to represent the flow fields grows without saturation, in contrast to the plateauing of $χ$ reported for velocity fields in isothermal 2D turbulence. Crucially, however, dynamical simulations solving the governing equations directly in the compressed MPS format at fixed $χ$ show that the $χ$ required to recover statistical observables, such as the Nusselt number, scales significantly more favorably with $\mathrm{Ra}$ than the a priori complexity suggests. At $\mathrm{Ra} = 10^{10}$, a relative error of $1.8\%$ in the mean Nusselt number is achieved with a nearly 9-fold reduction in degrees of freedom, using a $χ$ comparable to that required at $\mathrm{Ra} = 10^{9}$. Spectral analysis confirms the progressive recovery of spatial and temporal scales with increasing $χ$. These findings establish MPS as a scalable tool for simulating thermally driven turbulence, suggesting the method may remain viable for investigations of the ultimate regime at substantially higher $\mathrm{Ra}$.
title Quantum-Inspired Simulation of 2D Turbulent Rayleigh-Bénard Convection
topic Fluid Dynamics
Computational Physics
Quantum Physics
url https://arxiv.org/abs/2604.16179