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

• URL: http://arxiv.org/abs/2604.16179v1
• Date: Fri, 17 Apr 2026 15:46:29 GMT
• Title: Quantum-Inspired Simulation of 2D Turbulent Rayleigh-Bénard Convection
• Abstract summary: Turbulent thermal convection governs heat transport in systems ranging from stellar interiors to industrial heat exchangers.<n>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.<n>We apply Matrix Product State (MPS) methods to two-dimensional Rayleigh-Bénard convection with dynamical simulations up to $mathrmRa = 1010$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\mathrm{Ra}$.

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