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Related papers: Weighted reduced order methods for uncertainty qua…

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In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We…

Numerical Analysis · Mathematics 2023-08-08 Luca Venturi , Davide Torlo , Francesco Ballarin , Gianluigi Rozza

In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems.…

Numerical Analysis · Mathematics 2023-08-08 Luca Venturi , Francesco Ballarin , Gianluigi Rozza

The numerical simulation of incompressible flows is challenging due to the tight coupling of velocity and pressure. Projection methods offer an effective solution by decoupling these variables, making them suitable for large-scale…

Numerical Analysis · Mathematics 2025-12-12 Mejdi Azaïez , Yayu Guo , Carlos Núñez Fernández , Samuele Rubino , Chuanju Xu

We present two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a…

Numerical Analysis · Mathematics 2023-08-08 Saddam Hijazi , Shafqat Ali , Giovanni Stabile , Francesco Ballarin , Gianluigi Rozza

Computational fluid dynamics (CFD) simulations play an important role in engineering science and applications, however, it is not applicable for problems requiring a large number of repeated calculations. Accordingly, many reduced-order…

Fluid Dynamics · Physics 2026-05-28 Shan Ding , Yongfu Tian , Rui Yang

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…

Numerical Analysis · Mathematics 2017-09-28 Max Gunzburger , Nan Jiang , Michael Schneier

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Zakia Zainib , Francesco Ballarin , Gianluigi Rozza

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

The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…

Numerical Analysis · Mathematics 2025-08-12 Dominic Breit , Andreas Prohl , Jörn Wichmann

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…

Fluid Dynamics · Physics 2013-09-11 Maciej Balajewicz , Earl Dowell , Bernd Noack

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…

Fluid Dynamics · Physics 2024-05-31 Matteo Zancanaro , Valentin Nkana Ngan , Giovanni Stabile , Gianluigi Rozza

This work deals with the investigation of bifurcating fluid phenomena using a reduced order modelling setting aided by artificial neural networks. We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear…

Fluid Dynamics · Physics 2023-08-08 Federico Pichi , Francesco Ballarin , Gianluigi Rozza , Jan S. Hesthaven

Reduced order methods (ROMs) for the incompressible Navier--Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the temporal derivative of the velocity from a full order mixed…

Numerical Analysis · Mathematics 2023-04-18 Bosco García-Archilla , Volker John , Sarah Katz , Julia Novo

In this work we introduce and analyse a new low-order method for the variable-density incompressible Navier-Stokes equations. The main novelty of the proposed method lies in the support of general meshes, possibly including polygonal or…

Numerical Analysis · Mathematics 2026-01-22 Mathias Dauphin , Daniele A. Di Pietro , Jérôme Droniou , Alexandros Skouras

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

We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier--Stokes dynamics as a state-space model and to view…

Computation · Statistics 2026-02-04 Nicholas Polson , Vadim Sokolov

A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…

Numerical Analysis · Mathematics 2022-05-02 Jad Doghman

We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is based on transforming the system into a partial…

Analysis of PDEs · Mathematics 2025-04-15 D. Breit , E. Feireisl , M. Hofmanova , P. B. Mucha

In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier-Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a…

Numerical Analysis · Mathematics 2019-02-08 Giovanni Stabile , 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…

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