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We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced…

Optimization and Control · Mathematics 2015-05-13 Sunil Ahuja , Clarence W. Rowley

The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations…

Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…

Fluid Dynamics · Physics 2021-10-13 Pranshu Pant , Ruchit Doshi , Pranav Bahl , Amir Barati Farimani

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…

Computational Engineering, Finance, and Science · Computer Science 2026-01-26 Alejandro N Diaz , Shane A McQuarrie , John T Tencer , Patrick J Blonigan

We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order…

Numerical Analysis · Mathematics 2013-06-13 François Bouchut , Sébastien Boyaval

We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids,…

Numerical simulations are a valuable research and layout tool for fluid flow problems, yet repeated evaluations of parametrized problems, necessary to solve optimization problems, can be very costly. One option to speed up this process is…

Fluid Dynamics · Physics 2025-02-28 Marian Staggl , Wolfgang Sanz , Paul Pieringer

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for…

Computational Engineering, Finance, and Science · Computer Science 2018-10-25 J. Nagoor Kani , Ahmed H. Elsheikh

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation…

Numerical Analysis · Mathematics 2020-02-05 Vasileios Tsiolakis , Matteo Giacomini , Ruben Sevilla , Carsten Othmer , Antonio Huerta

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

Numerical Analysis · Mathematics 2024-06-07 Anna Ivagnes , Giovanni Stabile , Gianluigi Rozza

Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic…

Dynamical Systems · Mathematics 2020-12-09 Peter Benner , Pawan Goyal , Jan Heiland , Igor Pontes Duff

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…

Vortex-induced vibrations (VIV) pose computationally expensive problems of high practical interest to several engineering fields. In this work we develop a non-intrusive, reduced-order modelling methodology for two-dimensional (2D) VIV…

Fluid Dynamics · Physics 2024-04-04 Leonidas Gkimisis , Thomas Richter , Peter Benner

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…

Computational Physics · Physics 2019-09-04 S. Pawar , S. M. Rahman , H. Vaddireddy , O. San , A. Rasheed , P. Vedula

We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach…

Numerical Analysis · Mathematics 2024-03-07 Enrico Ballini , Luca Formaggia , Alessio Fumagalli , Anna Scotti , Paolo Zunino

Data-driven modeling for nonlinear fluid flows using sparse convolution-based mapping into a feature space where the dynamics are Markov linear is explored in this article. The underlying principle of low-order models for fluid systems is…

Fluid Dynamics · Physics 2020-10-28 Chen Lu , Balaji Jayaraman , Joshua Whitman , Girish Chowdhary

We propose a Hybrid High-Order (HHO) formulation of the incompressible Navier-Stokes equations with variable density that provides exact conservation of volume and, accordingly, pure advection of the density variable. The spatial…

Fluid Dynamics · Physics 2026-05-14 Lorenzo Botti , Francesco Carlo Massa

This work introduces a data-driven, non-intrusive reduced-order modeling (ROM) framework that leverages Optimal Transport (OT) for multi-fidelity and parametric problems in two-phase flows modelling. Building upon the success of…

Numerical Analysis · Mathematics 2026-03-30 Moaad Khamlich , Niccolò Tonicello , Federico Pichi , Gianluigi Rozza

In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…

In this work, we propose a framework that constructs reduced order models for nonlinear structural mechanics in a nonintrusive fashion, and can handle large scale simulations. We identify three steps that are carried out separately in time,…

Numerical Analysis · Mathematics 2023-02-02 Fabien Casenave , Nissrine Akkari , Felipe Bordeu , Christian Rey , David Ryckelynck
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