# A segregated reduced-order model of a pressure-based solver for turbulent compressible flows

## TL;DR

This paper introduces a new reduced-order model for simulating turbulent compressible flows using segregated solvers and data-driven methods.

## Contribution

The novel approach combines segregated solvers with data-driven interpolation to create a turbulence model-independent reduced-order framework.

## Key findings

- Segregated reduced-order models can accurately predict high Reynolds and Mach number flows.
- Hybrid methods using neural networks or interpolation improve accuracy over traditional Galerkin projection.
- The framework maintains accuracy while being independent of specific turbulence models.

## Abstract

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing closely accurate solutions with respect to the high fidelity flow fields. Full-order solutions are often obtained through the use of segregated solvers (solution variables are solved one after another), employing slightly modified conservation laws so that they can be decoupled and then solved one at a time. Classical reduction architectures, on the contrary, rely on the Galerkin projection of a complete Navier–Stokes system to be projected all at once, causing a mild discrepancy with the high order solutions. This article relies on segregated reduced-order algorithms for the resolution of turbulent and compressible flows in the context of physical and geometrical parameters. At the full-order level turbulence is modeled using an eddy viscosity approach. Since there is a variety of different turbulence models for the approximation of this supplementary viscosity, one of the aims of this work is to provide a reduced-order model which is independent on this selection. This goal is reached by the application of hybrid methods where Navier–Stokes equations are projected in a standard way while the viscosity field is approximated by the use of data-driven interpolation methods or by the evaluation of a properly trained neural network. By exploiting the aforementioned expedients it is possible to predict accurate solutions with respect to the full-order problems characterized by high Reynolds numbers and elevated Mach numbers.