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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

In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier-Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and…

Numerical Analysis · Mathematics 2018-02-26 Daniele A. Di Pietro , Stella Krell

In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…

Numerical Analysis · Mathematics 2023-01-16 Erik Burman , Deepika Garg , Janosch Preuss

We construct high-order semi-discrete-in-time and fully discrete (with Fourier-Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary conditions, and carry out corresponding error analysis. The…

Numerical Analysis · Mathematics 2021-03-23 Fukeng Huang , Jie Shen

In this paper, we develop and analyze a novel numerical scheme for the steady incompressible Navier-Stokes equations by the weak Galerkin methods. The divergence-preserving velocity reconstruction operator is employed in the discretization…

Numerical Analysis · Mathematics 2020-11-24 Lin Mu

The goal of this paper is to create a fruitful bridge between the numerical methods for approximating partial differential equations (PDEs) in fluid dynamics and the (iterative) numerical methods for dealing with the resulting large linear…

Numerical Analysis · Mathematics 2016-12-15 M. Dumbser , F. Fambri , I. Furci , M. Mazza , M. Tavelli , S. Serra-Capizzano

We propose a novel collocated projection method for solving the incompressible Navier-Stokes equations with arbitrary boundaries. Our approach employs non-graded octree grids, where all variables are stored at the nodes. To discretize the…

Numerical Analysis · Mathematics 2025-06-04 Matthew Blomquist , Scott R. West , Adam L. Binswanger , Maxime Theillard

This paper presents an enriched Galerkin (EG) finite element method for the incompressible Navier--Stokes equations. The method augments continuous piecewise linear velocity spaces with elementwise bubble functions, yielding a locally…

Numerical Analysis · Mathematics 2025-11-26 Chun Song , Minfu Feng

This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…

Numerical Analysis · Mathematics 2025-12-22 Suyash Shrestha , Marc Gerritsma , Gonzalo Rubio , Steven Hulshoff , Esteban Ferrer

In this work we propose a novel Hybrid High-Order method for the incompressible Navier--Stokes equations based on a formulation of the convective term including Temam's device for stability. The proposed method has several advantageous…

Numerical Analysis · Mathematics 2018-10-11 Lorenzo Botti , Daniele Di Pietro , Jérôme Droniou

We propose and analyze a finite element method for a semi-stationary Stokes system modeling compressible fluid flow subject to a Navier-slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element…

Numerical Analysis · Mathematics 2009-04-07 Kenneth H. Karlsen , Trygve K. Karper

In this paper, we are interested in constructing a scheme solving compressible Navier--Stokes equations, with desired properties including high order spatial accuracy, conservation, and positivity-preserving of density and internal energy…

Numerical Analysis · Mathematics 2023-09-13 Chen Liu , Xiangxiong Zhang

Purpose: This study aims to assess the accuracy of degree adaptive strategies in the context of incompressible Navier-Stokes flows using the high order hybridisable discontinuous Galerkin (HDG) method. Design/methodology/approach: The work…

Fluid Dynamics · Physics 2024-11-12 Agustina Felipe , Ruben Sevilla , Oubay Hassan

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

The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows. Although many highly efficient algorithms have been proposed for simulating each type of the flows, the…

Computational Physics · Physics 2018-10-04 Roman Frolov

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

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…

Numerical Analysis · Mathematics 2014-12-04 Maurizio Tavelli , Michael Dumbser

This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The…

Computational Physics · Physics 2019-09-04 Nishant Nangia , Boyce E. Griffith , Neelesh A. Patankar , Amneet Pal Singh Bhalla

The purpose of this work is to present a reduced order modeling framework for parametrized turbulent flows with moderately high Reynolds numbers within the variational multiscale (VMS) method. The Reduced Order Models (ROMs) presented in…

Numerical Analysis · Mathematics 2023-08-08 Giovanni Stabile , Francesco Ballarin , Giacomo Zuccarino , Gianluigi Rozza

Geometrically parametrized Partial Differential Equations are nowadays widely used in many different fields as, for example, shape optimization processes or patient specific surgery studies. The focus of this work is on some advances for…

Fluid Dynamics · Physics 2021-07-21 Matteo Zancanaro , Markus Mrosek , Giovanni Stabile , Carsten Othmer , Gianluigi Rozza