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Tlales, KAuthorTlales, KenzaAuthorKheir-Eddine, OtmaniAuthorNtoukas, GAuthorNtoukas, GerasimosAuthorFerrer, EAuthor

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

Publicated to:Engineering With Computers. 40 (5): 2947-2969 - 2024-10-01 40(5), DOI: 10.1007/s00366-024-01950-y

Authors: Tlales, K; Otmani, KE; Ntoukas, G; Rubio, G; Ferrer, E

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Abstract

We present a machine learning-based mesh refinement technique for steady and unsteady incompressible flows. The clustering technique proposed by Otmani et al. (Phys Fluids 35(2):027112, 2023) is used to mark the viscous and turbulent regions for the flow past a cylinder at Re=40\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=40$$\end{document} (steady laminar flow), at Re=100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=100$$\end{document} (unsteady laminar flow), and at Re=3900\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=3900$$\end{document} (unsteady turbulent flow). Within this clustered region, we use high mesh resolution, while downgrading the resolution outside, to show that it is possible to obtain levels of accuracy similar to those obtained when using a uniformly refined mesh. The mesh adaptation is effective, as the clustering successfully identifies the two flow regions, a viscous/turbulent dominated region (including the boundary layer and wake) that requires high resolution and an inviscid/irrotational region, which only requires low resolution. The new clustering sensor is compared with traditional feature-based sensors (Q-criterion and vorticity based) commonly used for mesh adaptation. Unlike traditional sensors that rely on problem-dependent thresholds, our novel approach eliminates the need for such thresholds and locates the regions that require adaptation. After the initial validation using flows past cylinders, the clustering technique is applied in an engineering context to study the flow around a horizontal axis wind turbine configuration which has been tested experimentally at the Norwegian University of Science and Technology. 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 laminar test cases, we can reduce the computational cost by 32% (steady Re=40\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=40$$\end{document} case) and 20% (unsteady Re=100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=100$$\end{document} case), while we get a reduction of 33% for the Re=3900\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=3900$$\end{document} turbulent case. In the context of the wind turbine, a reduction of 43% in computational cost is observed, while maintaining the accuracy.

Keywords

Circular-cylinderClusteringDiscontinuous galerkinDynamicsErrorsLarge eddy simulationLarge-eddy simulationMachine learningMesh refinementNavier-stokes equationsNavier–stokes equationsRefinementSteadyStrategiesTruncationUnsupervised learningWake

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Engineering With Computers due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 15/170, thus managing to position itself as a Q1 (Primer Cuartil), in the category Computer Science, Interdisciplinary Applications. Notably, the journal is positioned above the 90th percentile.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-06-01:

  • Google Scholar: 12
  • WoS: 3
  • Scopus: 9

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-01:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 12 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

    It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

    • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
    • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/86474/

    As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

    • Views: 39
    • Downloads: 8

    Leadership analysis of institutional authors

    There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (TLALES, KENZA) and Last Author (FERRER VACCAREZZA, ESTEBAN).

    the author responsible for correspondence tasks has been Rubio, G.