# Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM

## TL;DR

This paper introduces a nonintrusive proper generalised decomposition (PGD) method integrated into OpenFOAM, enabling efficient parametric flow simulations with minimal online computational cost, suitable for industrial applications.

## Contribution

It presents the first nonintrusive PGD implementation in OpenFOAM, combining reduced order modeling with industrial CFD tools for parametrised incompressible flow problems.

## Key findings

- Successful application to 2D and 3D laminar flow benchmarks
- Efficient parametric interpolation without additional solves
- Demonstrated industrial relevance with automotive flow control

## Abstract

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier-Stokes equations. The key feature of this approach is the seamless integration of a reduced order model (ROM) in the framework of an industrially validated computational fluid dynamics software. This is of special importance in an industrial environment because in the online phase of the PGD ROM the description of the flow for a specific set of parameters is obtained simply via interpolation of the generalised solution, without the need of any extra solution step. On the one hand, the spatial problems arising from the PGD separation of the unknowns are treated using the classical solution strategies of OpenFOAM, namely the semi-implicit method for pressure linked equations (SIMPLE) algorithm. On the other hand, the parametric iteration is solved via a collocation approach. The resulting ROM is applied to several benchmark tests of laminar incompressible Navier-Stokes flows, in two and three dimensions, with different parameters affecting the flow features. Eventually, the capability of the proposed strategy to treat industrial problems is verified by applying the methodology to a parametrised flow control in a realistic geometry of interest for the automotive industry.