Machine learning adaptation for laminar and turbulent flows: applications to high order discontinuous Galerkin solvers

TL;DR

This paper introduces a machine learning-based mesh refinement method that adaptively increases polynomial order in flow regions, achieving accuracy comparable to uniform refinement while reducing computational costs in high-order discontinuous Galerkin simulations.

Contribution

It presents a novel clustering-based adaptive p-refinement technique for high-order DG solvers applied to laminar and turbulent flows, improving efficiency and accuracy.

Findings

Achieved up to 32% reduction in computational cost for laminar flow.

Achieved up to 33% reduction in computational cost for turbulent flow.

Successfully identified viscous/turbulent and inviscid flow regions using clustering.

Abstract

We present a machine learning-based mesh refinement technique for steady and unsteady flows. The clustering technique proposed by Otmani et al. arXiv:2207.02929 [physics.flu-dyn] is used to mark the viscous and turbulent regions for the flow past a cylinder at Re=40 (steady laminar flow) and Re=3900 (unsteady turbulent flow). Within this clustered region, we increase the polynomial order to show that it is possible to obtain similar levels of accuracy to a uniformly refined mesh. The method is effective as the clustering successfully identifies the two flow regions, a viscous/turbulent dominated region (including the boundary layer and wake) and an inviscid/irrotational region (a potential flow region). The data used within this framework are generated using a high-order discontinuous Galerkin solver, allowing to locally refine the polynomial order (p-refinement) in each element of the clustered region. For the steady laminar test case we are able to reduce the computational cost up to 32% and for the unsteady turbulent case up to 33%.