State estimation of Rayleigh-B\'enard convection with reduced-order models

Physics > Fluid Dynamics [Submitted on 18 Jun 2026] Title:State estimation of Rayleigh-Bénard convection with reduced-order models View PDF HTML (experimental)Abstract:In this work, we develop a state estimation framework for two-dimensional Rayleigh-Bénard (RB) convection that combines a stable Galerkin reduced-order model (ROM) with an extended Kalman filter (EKF). The ROM, constructed from controllability modes of the linearised Boussinesq equations, provides the nonlinear dynamical model for the filter prediction step. Direct numerical simulations (DNS) are used to generate synthetic measurements for data assimilation. We assess filter performance across periodic, quasiperiodic, and chaotic regimes, demonstrating that the filter tracks the most energetic modes with high fidelity and achieves time-averaged reconstruction errors below $14\%$ for velocity and $9\%$ for temperature. We apply the ROM-based EKF to a hybrid simulation scenario where the system state is assimilated from coarse PIV-like velocity measurements. It is shown that velocity observations alone suffice to reconstruct the state, including the temperature field. Finally, we exploit the Kalman gain matrix to develop a greedy sensor placement strategy that progressively removes the least informative sensors. The algorithm reveals a clear hierarchy among sensor types and can be used to derive skeletal observation configurations. It also provides guidance on which measurement variables and spatial locations are most informative for state correction. The present framework is general, and may be applied to other quadratic Galerkin ROMs for state estimation. Submission history From: Enrique Flores-Montoya [view email][v1] Thu, 18 Jun 2026 17:28:57 UTC (5,245 KB) Current browse context: physics.flu-dyn Change to browse by: References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.