Reduced-Order Time Splitting for Navier-Stokes with Open Boundaries

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Main Authors: Azaïez, Mejdi, Rebollo, Tomás Chacón, Fernández, Carlos Núñez, Rubino, Samuele
Format: Preprint
Published: 2025
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author Azaïez, Mejdi
Rebollo, Tomás Chacón
Fernández, Carlos Núñez
Rubino, Samuele
author_facet Azaïez, Mejdi
Rebollo, Tomás Chacón
Fernández, Carlos Núñez
Rubino, Samuele
contents 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 reduce the computing time to solve NSE: time splitting, reduction of the computational domain through non-standard treatment of open boundary conditions and reduced order modelling. To make the work self-contained, we first present the formulation of the time-splitting scheme applied to the Navier-Stokes equations with open boundary conditions, employing a first-order Euler time discretization and deriving the non-standard boundary condition for pressure. Then, we construct a Galerkin projection-based ROM using POD with two different treatments of the pressure boundary condition on the outlet. We propose a comparative performance analysis between the standard projection-based POD-ROM (fully intrusive) and a hybrid POD-ROM that combines a projection-based approach (intrusive) with a data-driven technique (non-intrusive) using Radial Basis Functions (RBF). We illustrate this comparison through two different numerical tests: the flow in a bifurcated tube and the benchmark numerical test of the flow past cylinder, numerically investigating the efficiency and accuracy of both ROMs.
format Preprint
id arxiv_https___arxiv_org_abs_2506_10763
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Reduced-Order Time Splitting for Navier-Stokes with Open Boundaries
Azaïez, Mejdi
Rebollo, Tomás Chacón
Fernández, Carlos Núñez
Rubino, Samuele
Numerical Analysis
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 reduce the computing time to solve NSE: time splitting, reduction of the computational domain through non-standard treatment of open boundary conditions and reduced order modelling. To make the work self-contained, we first present the formulation of the time-splitting scheme applied to the Navier-Stokes equations with open boundary conditions, employing a first-order Euler time discretization and deriving the non-standard boundary condition for pressure. Then, we construct a Galerkin projection-based ROM using POD with two different treatments of the pressure boundary condition on the outlet. We propose a comparative performance analysis between the standard projection-based POD-ROM (fully intrusive) and a hybrid POD-ROM that combines a projection-based approach (intrusive) with a data-driven technique (non-intrusive) using Radial Basis Functions (RBF). We illustrate this comparison through two different numerical tests: the flow in a bifurcated tube and the benchmark numerical test of the flow past cylinder, numerically investigating the efficiency and accuracy of both ROMs.
title Reduced-Order Time Splitting for Navier-Stokes with Open Boundaries
topic Numerical Analysis
url https://arxiv.org/abs/2506.10763