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This paper is on the construction of structure-preserving, online-efficient reduced models for the barotropic Euler equations with a friction term on networks. The nonlinear flow problem finds broad application in the context of gas…

Numerical Analysis · Mathematics 2021-10-12 Björn Liljegren-Sailer , Nicole Marheineke

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

Computational Physics · Physics 2021-02-03 Elizabeth H. Krath , Forrest L. Carpenter , Paul G. A. Cizmas , David A. Johnston

This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…

Numerical Analysis · Computer Science 2018-07-04 Kevin Carlberg , Youngsoo Choi , Syuzanna Sargsyan

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous…

Numerical Analysis · Mathematics 2022-01-04 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for numerical simulations of compressible flows. This paper presents an overview of the recent development of DG methods for compressible…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

Machine Learning · Computer Science 2021-07-07 Sourav Dutta , Peter Rivera-Casillas , Orie M. Cecil , Matthew W. Farthing , Emma Perracchione , Mario Putti

Reduced-order models (ROMs) are widely used in fluid engineering to enable rapid prediction of flow fields for parametric analysis, design optimization, and control applications. Proper orthogonal decomposition (POD) is commonly employed to…

Fluid Dynamics · Physics 2026-02-25 Yuto Nakamura , Shintaro Sato , Naofumi Ohnishi

We propose a novel method for model-based time super-sampling of turbulent flow fields. The key enabler is the identification of an empirical Galerkin model from the projection of the Navier-Stokes equations on a data-tailored basis. The…

In this work, we introduce two novel reformulations of a recent weakly hyperbolic model for two-phase flow with surface tension. In the model, the tracking of phase boundaries is achieved by using a vector interface field, rather than a…

Numerical Analysis · Mathematics 2021-02-03 Simone Chiocchetti , Ilya Peshkov , Sergey Gavrilyuk , Michael Dumbser

In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) for the optimal control of the convective…

Numerical Analysis · Mathematics 2020-05-28 Bülent Karasözen , Murat Uzunca , Tuğba Küçükseyhan

The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear model reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with…

Numerical Analysis · Mathematics 2014-11-06 Kevin Carlberg , Charbel Farhat , Julien Cortial , David Amsallem

We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the…

Numerical Analysis · Mathematics 2017-02-08 Bülent Karasözen , Murat Uzunca , Tuğba Küçükseyhan

This article presents a Galerkin projection-based reduced-order modelling (ROM) approach for segregated fluid-structure interaction (FSI) problems, formulated within an Arbitrary Lagrangian Eulerian (ALE) framework at low Reynolds numbers…

Numerical Analysis · Mathematics 2025-07-24 Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

This article investigates matrix-free higher-order discontinuous Galerkin discretizations of the Navier--Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a…

Computational Engineering, Finance, and Science · Computer Science 2025-11-04 Richard Schussnig , Niklas Fehn , Douglas Ramalho Queiroz Pacheco , Martin Kronbichler

In this paper, an end-to-end nonlinear model reduction methodology is presented based on the convolutional recurrent autoencoder networks. The methodology is developed in the context of the overall data-driven reduced-order model framework…

Fluid Dynamics · Physics 2020-03-30 Sandeep Reddy Bukka , Allan Ross Magee , Rajeev Kumar Jaiman

Low-temperature plasmas often present non-equilibrium ion distribution functions due to the collisions with the background gas and the presence of strong electric fields. This non-equilibrium is beyond classical fluid models, often…

Plasma Physics · Physics 2025-10-31 Anatole Berger , Thierry Magin , Anne Bourdon , Alejandro Alvarez Laguna

We propose a new family of high order staggered semi-implicit discontinuous Galerkin (DG) methods for the simulation of natural convection problems. Assuming small temperature fluctuations, the Boussinesq approximation is valid and the flow…

Computational Physics · Physics 2019-12-05 Saray Busto , Maurizio Tavelli , Walter Boscheri , Michael Dumbser

The present work compares results for different numerical methods in search of alternatives to improve the quality of large-eddy simulations for the problem of supersonic turbulent jet flows. Previous work has analyzed supersonic jet flows…

Fluid Dynamics · Physics 2025-09-23 D. F. Abreu , C. Junqueira-Junior , E. T. V. Dauricio , J. L. F. Azevedo

Reduced-order models (ROMs) of turbulent flows based on Galerkin projection often require many degrees of freedom to resolve the dynamics of the turbulence, or simulation data to obtain an optimal modal basis. However, obtaining simulation…

Fluid Dynamics · Physics 2025-11-21 Ian Addison-Smith , Igor A. Maia , Benjamin Herrmann , Andre V. G. Cavalieri

Galerkin reduced order models (ROMs), e.g., based on proper orthogonal decomposition (POD) or reduced basis methods, have achieved significant success in the numerical simulation of fluid flows. The ROM numerical analysis, however, is still…

Numerical Analysis · Mathematics 2024-09-04 Francesco Ballarin , Traian Iliescu