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Meshfree solution schemes for the incompressible Navier--Stokes equations are usually based on algorithms commonly used in finite volume methods, such as projection methods, SIMPLE and PISO algorithms. However, drawbacks of these algorithms…

Numerical Analysis · Mathematics 2018-02-02 Pratik Suchde , Joerg Kuhnert , Sudarshan Tiwari

Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two but the novel…

Fluid Dynamics · Physics 2020-01-29 Shady E. Ahmed , Sk. Mashfiqur Rahman , Omer San , Adil Rasheed , Ionel M. Navon

Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…

Numerical Analysis · Mathematics 2023-07-04 Jun Sur Richard Park , Xueyu Zhu

In this paper, we propose a nonintrusive filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier-Stokes equations in convection-dominated regimes. We propose a novel…

Numerical Analysis · Mathematics 2018-10-23 M. Gunzburger , T. Iliescu , M. Mohebujjaman , M. Schneier

In recent years, numerical methods in industrial applications have evolved from a pure predictive tool towards a means for optimization and control. Since standard numerical analysis methods have become prohibitively costly in such…

Computational Physics · Physics 2021-04-23 Artūrs Bērziņš , Jan Helmig , Fabian Key , Stefanie Elgeti

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…

Numerical Analysis · Mathematics 2022-12-21 Niccolò Tonicello , Andrea Lario , Gianluigi Rozza , Gianmarco Mengaldo

This work introduces RedEigCD, the first self-adaptive timestepping technique specifically tailored for reduced-order models (ROMs) of the incompressible Navier-Stokes equations. Building upon linear stability concepts, the method adapts…

Numerical Analysis · Mathematics 2026-04-22 Josep Plana-Riu , Henrik Rosenberger , Benjamin Sanderse , F. Xavier Trias

The work provides an integrated pipeline for the model order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, Free-Form Deformation is applied for geometry parametrisation, whereas two different…

Numerical Analysis · Mathematics 2018-03-15 F. Salmoiraghi , A. Scardigli , H. Telib , G. Rozza

We consider iterative methods for solving the linearised Navier-Stokes equations arising from two-phase flow problems and the efficient preconditioning of such systems when using mixed finite element methods. Our target application is…

Numerical Analysis · Mathematics 2020-05-18 Niall Bootland , Alistair Bentley , Christopher Kees , Andrew Wathen

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based…

Computational Physics · Physics 2016-08-24 Maciej Balajewicz , Irina Tezaur , Earl Dowell

Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective…

Numerical Analysis · Mathematics 2024-06-05 Guglielmo Padula , Michele Girfoglio , Gianluigi Rozza

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

We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated…

Computational Engineering, Finance, and Science · Computer Science 2021-12-13 Zizhou Huang , Teseo Schneider , Minchen Li , Chenfanfu Jiang , Denis Zorin , Daniele Panozzo

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method…

Fluid Dynamics · Physics 2025-08-22 Xinjie Ji , Changxiao Nigel Shen , Wim M. van Rees

This paper presents a reduced order approach for transient modeling of multiple moving objects in nonlinear crossflows. The Proper Orthogonal Decomposition method and the Galerkin projection are used to construct a reduced version of the…

Fluid Dynamics · Physics 2021-06-07 My Ha Dao

Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…

Mathematical Physics · Physics 2025-06-06 Ricardo Costa , Stéphane Clain , Gaspar J. Machado , João M. Nóbrega

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Machine Learning · Computer Science 2026-01-16 Andrew F. Ilersich , Kevin Course , Prasanth B. Nair

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical…

Fluid Dynamics · Physics 2024-05-07 J. R. Bravo , G. Stabile , M. Hess , J. A. Hernandez , R. Rossi , G. Rozza

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

Numerical Analysis · Mathematics 2025-06-11 M. A. Freitag , J. M. Nicolaus , M. Redmann

We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier--Stokes equations (NSE). In the proposed approach, the presence of simulated…

Fluid Dynamics · Physics 2022-09-08 Saddam Hijazi , Melina Freitag , Niels Landwehr