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

TL;DR

This paper introduces a reduced-order modeling approach combining time splitting, domain reduction, and POD techniques to efficiently solve Navier-Stokes equations with open boundaries, validated through numerical tests.

Contribution

It develops a hybrid POD-ROM that integrates intrusive and non-intrusive methods for improved efficiency and accuracy in open boundary flow simulations.

Findings

Hybrid POD-ROM outperforms standard in accuracy.

Reduced computational time demonstrated in numerical tests.

Effective handling of open boundary conditions achieved.

Abstract

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.