A Novel Model Order Reduction Approach for Navier-Stokes Equations at High Reynolds Number

Abstract

A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the training data set, the new basis functions also provide stable and accurate reduced-order models. The proposed approach is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer.

References in corpus (2)

• Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison
• Singular Value Decomposition and Principal Component Analysis

Cited by in corpus (42)

• Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation
• On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows
• Study of dynamics in post-transient flows using Koopman mode decomposition
• Conservative model reduction for finite-volume models
• Physics-constrained, low-dimensional models for MHD: First-principles and data-driven approaches
• Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations
• Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems
• A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation
• Proper orthogonal decomposition closure models for fluid flows: Burgers equation
• On a certified Smagorinsky reduced basis turbulence model
• On the role of nonlinear correlations in reduced-order modeling
• Optimal Nonlinear Eddy Viscosity in Galerkin Models of Turbulent Flows
• Dimensionality Reduction and Reduced Order Modeling for Traveling Wave Physics
• A data-driven Koopman model predictive control framework for nonlinear flows
• Reduction of Nonlinear Embedded Boundary Models for Problems with Evolving Interfaces
• Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods
• A Multifidelity deep operator network approach to closure for multiscale systems
• Regularized Reduced Order Models for a Stochastic Burgers Equation
• Model Order Reduction in Neuroscience
• Preserving general physical properties in model reduction of dynamical systems via constrained-optimization projection
• Phase proper orthogonal decomposition of non-stationary turbulent flow
• An Optimal Model Identification For Oscillatory Dynamics With a Stable Limit Cycle
• Data-Driven Filtered Reduced Order Modeling Of Fluid Flows
• Promoting global stability in data-driven models of quadratic nonlinear dynamics
• Lyapunov stable Galerkin models of post-transient incompressible flows
• Constrained Sparse Galerkin Regression
• The structure of global conservation laws in Galerkin plasma models
• Learning-based Reduced Order Model Stabilization for Partial Differential Equations: Application to the Coupled Burgers Equation
• WaveRange: Wavelet-based data compression for three-dimensional numerical simulations on regular grids
• An Evolve-Then-Filter Regularized Reduced Order Model
• Robust Reduced-Order Model Stabilization for Partial Differential Equations Based on Lyapunov Theory and Extremum Seeking with Application to the 3D Boussinesq Equations
• Structure-preserving model reduction for marginally stable LTI systems
• Approximate Deconvolution Reduced Order Modeling
• Non-intrusive inference reduced order model for fluids using linear multistep neural network
• Data-driven nonlinear aerodynamics models with certifiably optimal boundedness properties
• Projection-based model reduction for contact problems
• An efficient algorithm for simulating ensembles of parameterized MHD flow problems
• Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
• A-priori sparsification of Galerkin-based reduced order models
• $l_1$-based sparsification of energy interactions in two-dimensional turbulent flows