Hybrid neural network reduced order modelling for turbulent flows with geometric parameters

TL;DR

This paper introduces a hybrid neural network reduced order model combining Galerkin projection and data-driven methods to efficiently and accurately solve geometrically parametrized turbulent flow problems, demonstrated on two test cases.

Contribution

It presents a novel hybrid approach that integrates classical Galerkin projection with data-driven techniques for improved turbulence modeling in parametrized geometries.

Findings

Enhanced accuracy over previous methods

Effective on complex turbulent flow cases

Versatile for different geometrical configurations

Abstract

Geometrically parametrized Partial Differential Equations are nowadays widely used in many different fields as, for example, shape optimization processes or patient specific surgery studies. The focus of this work is on some advances for this topic, capable of increasing the accuracy with respect to previous approaches while relying on a high cost-benefit ratio performance. The main scope of this paper is the introduction of a new technique mixing up a classical Galerkin-projection approach together with a data-driven method to obtain a versatile and accurate algorithm for the resolution of geometrically parametrized incompressible turbulent Navier-Stokes problems. The effectiveness of this procedure is demonstrated on two different test cases: a classical academic back step problem and a shape deformation Ahmed body application. The results show into details the properties of the architecture we developed while exposing possible future perspectives for this work.