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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 investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D…

Numerical Analysis · Mathematics 2026-03-20 Rahul Halder , Arash Hajisharifi , Kabir Bakhshaei , Gianluigi Rozza

The accurate numerical simulation of high Reynolds number incompressible flows is a challenging topic in computational fluid dynamics. Classical inf-sup stable methods like the Taylor-Hood element or only $L^2$-conforming discontinuous…

Numerical Analysis · Mathematics 2019-12-24 Marian Piatkowski , Peter Bastian

In this work, we propose a Proper Orthogonal Decomposition-Reduced Order Model (POD-ROM) applied to time-splitting schemes for solving the Navier-Stokes equations with open boundary conditions. In this method, we combine three strategies to…

Numerical Analysis · Mathematics 2025-06-13 Mejdi Azaïez , Tomás Chacón Rebollo , Carlos Núñez Fernández , Samuele Rubino

Proper orthogonal decomposition (POD) stabilized methods for the Navier-Stokes equations are considered and analyzed. We consider two cases, the case in which the snapshots are based on a non inf-sup stable method and the case in which the…

Numerical Analysis · Mathematics 2020-06-02 Julia Novo , Samuele Rubino

The G-equation is a well-known model for studying front propagation in turbulent combustion. In this paper, we develop an efficient model reduction method for computing \textcolor{black}{regular solutions} of viscous G-equations in…

Numerical Analysis · Mathematics 2020-11-17 Haotian Gu , Jack Xin , Zhiwen Zhang

This paper deals with the development of a Reduced-Order Model (ROM) to investigate haemodynamics in cardiovascular applications. It employs the use of Proper Orthogonal Decomposition (POD) for the computation of the basis functions and the…

Numerical Analysis · Mathematics 2025-01-24 Pierfrancesco Siena , Pasquale Claudio Africa , Michele Girfoglio , Gianluigi Rozza

This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced…

Fluid Dynamics · Physics 2023-07-24 Cyrille Allery , Claudine Beghein , Claire Dubot , Fabien Dubot

The purpose of this work is to introduce a novel POD-Galerkin strategy for the hybrid finite volume/finite element solver introduced in Berm\'udez et al. 2014 and Busto et al. 2018. The interest is into the incompressible Navier-Stokes…

Numerical Analysis · Mathematics 2018-10-19 Saray Busto , Giovanni Stabile , Gianluigi Rozza , María Elena Vázquez-Cendón

We present a non-intrusive model reduction framework for linear poroelasticity problems in heterogeneous porous media using proper orthogonal decomposition (POD) and neural networks, based on the usual offline-online paradigm. As the…

Numerical Analysis · Mathematics 2023-08-08 T. Kadeethum , F. Ballarin , N. Bouklas

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

In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods.…

Numerical Analysis · Mathematics 2022-11-01 Bosco García-Archilla , Volker John , Julia Novo

We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier-Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a…

Numerical Analysis · Mathematics 2022-03-30 Bosco García-Archilla , Julia Novo , Samuele Rubino

We demonstrate exponential convergence of Reduced Order Model (ROM) approximations for mixed boundary value problems of the stationary, incompressible Navier-Stokes equations in plane, polygonal domains $\Omega$. Admissible boundary…

Numerical Analysis · Mathematics 2025-12-30 Francesco Romor , Federico Pichi , Giovanni Stabile , Gianluigi Rozza , Christoph Schwab

We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equations. The equations are discretized using a hybridizable…

Computational Engineering, Finance, and Science · Computer Science 2018-02-19 Maurice S. Fabien , Matthew G. Knepley , Beatrice M. Riviere

Classical Proper Orthogonal Decomposition (POD)-based Galerkin projection models of chaotic flows typically require a large number of modes as well as stabilization or closure terms to achieve adequate accuracy and long-term stability. We…

Computational Physics · Physics 2026-05-27 Anant Kumar , Oliver Morales , Rohit Deshmukh

We present a scalable and efficient iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an interplay between domain decomposition methods and HDG…

Numerical Analysis · Mathematics 2016-01-29 Sriramkrishnan Muralikrishnan , Minh-Binh Tran , Tan Bui-Thanh

In this paper, we propose an efficient proper orthogonal decomposition based reduced-order model(POD-ROM) for nonstationary Stokes equations, which combines the classical projection method with POD technique. This new scheme mainly owns two…

Numerical Analysis · Mathematics 2023-04-04 Xi Li , Yan Luo , Minfu Feng

In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The…

Numerical Analysis · Mathematics 2017-10-11 Fatma G. Eroglu , Songul Kaya , Leo G. Rebholz

We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the…

Fluid Dynamics · Physics 2016-05-04 Pablo Fernandez , Ngoc-Cuong Nguyen , Xevi Roca , Jaime Peraire