Long-time Reynolds averaging of reduced order models for fluid flows: Preliminary results

DOI10.3934/mine.2020001OpenAlexW2981970113MaRDI QIDQ2099367

Traian Iliescu, Birgul Koc, Luigi C. Berselli, Roger Lewandowski

Publication date: 23 November 2022

Published in: Mathematics in Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.04903

zbMATH Keywords

proper orthogonal decompositionBurgers equationlong-time behaviorStokes operatoreigenfunctionreduced order modelstatistical equilibrium problemtime-average energy exchange

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30)

Uses Software

• redbKIT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Control of Burgers equation by means of mode reduction
• Approximate deconvolution models of turbulence. Analysis, phenomenology and numerical analysis.
• Long-time turbulence model deduced from the Navier-Stokes equations
• Mathematical perspectives on large eddy simulation models for turbulent flows
• Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization
• Neural network closures for nonlinear model order reduction
• Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
• Statistical study of Navier-Stokes equations. I
• Algorithms and models for turbulence not at statistical equilibrium
• Approximate deconvolution reduced order modeling
• A conservative, second order, unconditionally stable artificial compression method
• An overview of projection methods for incompressible flows
• POD-based feedback control of the Burgers equation by solving the evolutionary HJB equation
• Certified reduced basis approximation for parametrized partial differential equations and applications
• Mathematical and numerical foundations of turbulence models and applications
• Are the Snapshot Difference Quotients Needed in the Proper Orthogonal Decomposition?
• Certified Reduced Basis Methods for Parametrized Partial Differential Equations
• Mathematics of Large Eddy Simulation of Turbulent Flows
• Finite Element Methods for Navier-Stokes Equations
• Intermodal energy transfers in a proper orthogonal decomposition–Galerkin representation of a turbulent separated flow
• Data-Driven Filtered Reduced Order Modeling of Fluid Flows
• HJB-POD-Based Feedback Design for the Optimal Control of Evolution Problems
• Model Order Reduction in Fluid Dynamics: Challenges and Perspectives
• On the Reynolds time-averaged equations and the long-time behavior of Leray–Hopf weak solutions, with applications to ensemble averages
• Fundamentals of reduced basis method for problems governed by parametrized PDEs and applications
• Proper orthogonal decomposition for optimality systems
• Reduced Basis Methods for Partial Differential Equations
• Galerkin proper orthogonal decomposition methods for parabolic problems