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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

We present a framework for optimal trajectory generation in flow-driven systems governed by the Navier-Stokes equations, combining a Proper Orthogonal Decomposition (POD) reduced0order model (ROM) with Model Predictive Control (MPC). The…

Optimization and Control · Mathematics 2025-12-01 Adam Waterman , Martin Guay

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

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, nonconvex obstacles, and the calculation of force…

Fluid Dynamics · Physics 2022-07-13 James Gabbard , Thomas Gillis , Philippe Chatelain , Wim M. van Rees

We prove the convergence of an incremental projection numerical scheme for the time-dependent incompressible Navier--Stokes equations, without any regularity assumption on the weak solution. The velocity and the pressure are discretised in…

Numerical Analysis · Mathematics 2023-06-30 Robert Eymard , David Maltese

A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…

Numerical Analysis · Mathematics 2014-11-27 F. Guillén-González , M. V. Redondo-Neble

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

The micropolar Rayleigh-B{\'e}nard convection system, which consists of Navier-Stokes equations, the angular momentum equation, and the heat equation, is a strongly nonlinear, coupled, and saddle point structural multiphysics system. A…

Numerical Analysis · Mathematics 2025-12-03 Ming Cui , Akang Hou , Xiaoyu Dong

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

Incompressible flow solvers based on strong-form meshfree methods represent arbitrary geometries without the need for a global mesh system. However, their local evaluations make it difficult to satisfy incompressibility at the discrete…

Numerical Analysis · Mathematics 2026-05-05 Takeharu Matsuda , Satoshi Ii

This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-in-time iterative decoupled algorithms, which incorporate…

Numerical Analysis · Mathematics 2025-08-07 Huipeng Gu , Francesco Ballarin , Mingchao Cai , Jingzhi Li

We consider a projection method for time-dependent incompressible Navier-Stokes equations with a total pressure boundary condition. The projection method is one of the numerical calculation methods for incompressible viscous fluids often…

Numerical Analysis · Mathematics 2021-06-03 Kazunori Matsui

We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear closure models are inspired from successful numerical stabilization techniques used in Large Eddy Simulations (LES), such as Local Projection…

Numerical Analysis · Mathematics 2017-11-28 Mejdi Azaïez , Tomás Chacón Rebollo , Samuele Rubino

Reduced-order models (ROMs) are widely used in fluid engineering to enable rapid prediction of flow fields for parametric analysis, design optimization, and control applications. Proper orthogonal decomposition (POD) is commonly employed to…

Fluid Dynamics · Physics 2026-02-25 Yuto Nakamura , Shintaro Sato , Naofumi Ohnishi

Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…

Numerical Analysis · Mathematics 2015-05-20 David Shirokoff , Rodolfo Ruben Rosales

This paper extends a low-rank tensor decomposition (LRTD) reduced order model (ROM) methodology to simulate viscous flows and in particular to predict a smooth branch of solutions for the incompressible Navier-Stokes equations.…

Fluid Dynamics · Physics 2024-05-08 Maxim A. Olshanskii , Leo G. Rebholz

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no…

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…

Numerical Analysis · Mathematics 2016-11-15 Nathaniel Trask , Martin Maxey , Xiaozhe Hu

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

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