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The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…

Computational Physics · Physics 2019-12-10 Jacek Szumbarski

We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded" reduced basis space, by applying proper orthogonal…

Numerical Analysis · Mathematics 2020-08-26 Efthymios N. Karatzas , Giovanni Stabile , Leo Nouveau , Guglielmo Scovazzi , Gianluigi Rozza

This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the motion of an incompressible homogeneous fluid in a bounded 2D or…

Numerical Analysis · Mathematics 2025-12-23 Zhanybek Baitulenov , Maxim Olshanskii , Almas Temirbekov , Nurlan Temirbekov , Syrym Kasenov

We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most…

Fluid Dynamics · Physics 2018-04-24 Marek Morzynski , Wojciech Szeliga , Bernd R. Noack

This paper deals with fast simulations of the haemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical…

Numerical Analysis · Mathematics 2018-01-19 Claudia M. Colciago , Simone Deparis

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

We introduce a widely applicable tensor network-based framework for developing reduced order models describing wall-bounded fluid flows. As a paradigmatic example, we consider the incompressible Navier-Stokes equations and the lid-driven…

Fluid Dynamics · Physics 2024-10-10 Martin Kiffner , Dieter Jaksch

Topology optimization of natural convection problems is computationally expensive, due to the large number of degrees of freedom (DOFs) in the model and its two-way coupled nature. Herein, a method is presented to reduce the computational…

Computational Engineering, Finance, and Science · Computer Science 2019-02-20 Janus Asmussen , Joe Alexandersen , Ole Sigmund , Casper Schousboe Andreasen

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

We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…

Numerical Analysis · Mathematics 2023-11-01 Tommaso Taddei , Xuejun Xu , Lei Zhang

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical…

Numerical Analysis · Mathematics 2023-11-09 Ivan Prusak , Monica Nonino , Davide Torlo , Francesco Ballarin , Gianluigi Rozza

Direct methods to obtain global stability modes are restricted by the daunting sizes and complexity of Jacobians encountered in general three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi methods have greatly…

Fluid Dynamics · Physics 2020-07-13 Rajesh Ranjan , S. Unnikrishnan , Datta Gaitonde

We consider model order reduction based on proper orthogonal decomposition (POD) for unsteady incompressible Navier-Stokes problems, assuming that the snapshots are given by spatially adapted finite element solutions. We propose two…

Numerical Analysis · Mathematics 2019-08-02 Carmen Gräßle , Michael Hinze , Jens Lang , Sebastian Ullmann

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 this paper, we propose a new stabilized projection-based POD-ROM for the numerical simulation of incompressible flows. The new method draws inspiration from successful numerical stabilization techniques used in the context of Finite…

Numerical Analysis · Mathematics 2019-07-23 Samuele Rubino

Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…

Numerical Analysis · Mathematics 2017-04-05 Howard C. Elman , Virginia Forstall

We consider a parameter estimation problem to determine the viscosity $\nu$ of a stochastically perturbed 2D Navier-Stokes system. We derive several different classes of estimators based on the first $N$ Fourier modes of a single sample…

Probability · Mathematics 2011-01-07 Igor Cialenco , Nathan Glatt-Holtz

PDE-constrained optimization is a field of numerical analysis that combines the theory of PDEs, nonlinear optimization and numerical linear algebra. Optimization problems of this kind arise in many physical applications, prominently in…

Numerical Analysis · Mathematics 2017-10-18 Gennadij Heidel , Andy Wathen

In this paper, both semidiscrete and fully discrete finite element methods are analyzed for the penalized two-dimensional unsteady Navier-Stokes equations with nonsmooth initial data. First order backward Euler method is applied for the…

Numerical Analysis · Mathematics 2026-04-16 Bikram Bir , Deepjyoti Goswami , Amiya K. Pani

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

Optimization and Control · Mathematics 2021-12-22 Adrien Taylor , Francis Bach