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Non‐Linear Reduced Order Modelling of Transonic Potential Flows for Fast Aerodynamic Analysis.

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Title: Non‐Linear Reduced Order Modelling of Transonic Potential Flows for Fast Aerodynamic Analysis.
Authors: Zuñiga, M.1,2 (AUTHOR), de Parga, S. Ares1,2 (AUTHOR), Zorrilla, R.1,2 (AUTHOR) rzorrilla@cimne.upc.edu, Rossi, R.1,2 (AUTHOR)
Source: International Journal for Numerical Methods in Engineering. 1/30/2026, Vol. 127 Issue 2, p1-26. 26p.
Subjects: Transonic flow, Aerodynamics, Reduced-order models, Proper orthogonal decomposition, Shock waves, Nonlinear analysis, Computational fluid dynamics, Galerkin methods
Abstract: This work presents a physics‐based reduced order modelling (ROM) framework for the efficient simulation of steady transonic potential flows around aerodynamic configurations. The approach leverages proper orthogonal decomposition and a least‐squares Petrov‐Galerkin (LSPG) projection to construct intrusive ROMs for the full potential equation. To improve accuracy in regions affected by strong gradients and shock waves, a spatially weighted LSPG formulation is introduced, yielding enhanced robustness compared to unweighted projection. The ROM training relies on a non‐linear β$$ \beta $$‐transformed Halton sampling of the parameter space, which concentrates samples in shock‐prone regimes and improves generalization without increasing offline cost. The methodology is implemented within the open‐source Kratos Multiphysics framework and validated on two benchmark configurations: the 2D NACA 0012 airfoil and the 3D ONERA M6 wing. The resulting ROMs achieve accurate reconstructions of aerodynamic fields and coefficients, with relative errors on the order of 10−3$$ 1{0}^{-3} $$, while reducing the dimensionality of the full order models by approximately three orders of magnitude. Although the corresponding speed‐ups (×2$$ \times 2 $$ in 2D and ×6.5$$ \times 6.5 $$ in 3D) remain modest for the present linear subspace setting, the results highlight the potential of physics‐based intrusive ROMs as reliable surrogates for transonic flows. In the shock‐dominated regimes examined, the proposed intrusive ROM provides more accurate and physically consistent solutions than standard data‐driven surrogates. The framework provides a solid baseline for future extensions incorporating hyper‐reduction and non‐linear ROM strategies. [ABSTRACT FROM AUTHOR]
Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Non‐Linear Reduced Order Modelling of Transonic Potential Flows for Fast Aerodynamic Analysis.
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  Data: <searchLink fieldCode="AR" term="%22Zuñiga%2C+M%2E%22">Zuñiga, M.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22de+Parga%2C+S%2E+Ares%22">de Parga, S. Ares</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zorrilla%2C+R%2E%22">Zorrilla, R.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> rzorrilla@cimne.upc.edu</i><br /><searchLink fieldCode="AR" term="%22Rossi%2C+R%2E%22">Rossi, R.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+for+Numerical+Methods+in+Engineering%22">International Journal for Numerical Methods in Engineering</searchLink>. 1/30/2026, Vol. 127 Issue 2, p1-26. 26p.
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  Data: <searchLink fieldCode="DE" term="%22Transonic+flow%22">Transonic flow</searchLink><br /><searchLink fieldCode="DE" term="%22Aerodynamics%22">Aerodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Reduced-order+models%22">Reduced-order models</searchLink><br /><searchLink fieldCode="DE" term="%22Proper+orthogonal+decomposition%22">Proper orthogonal decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Shock+waves%22">Shock waves</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+analysis%22">Nonlinear analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+fluid+dynamics%22">Computational fluid dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This work presents a physics‐based reduced order modelling (ROM) framework for the efficient simulation of steady transonic potential flows around aerodynamic configurations. The approach leverages proper orthogonal decomposition and a least‐squares Petrov‐Galerkin (LSPG) projection to construct intrusive ROMs for the full potential equation. To improve accuracy in regions affected by strong gradients and shock waves, a spatially weighted LSPG formulation is introduced, yielding enhanced robustness compared to unweighted projection. The ROM training relies on a non‐linear β$$ \beta $$‐transformed Halton sampling of the parameter space, which concentrates samples in shock‐prone regimes and improves generalization without increasing offline cost. The methodology is implemented within the open‐source Kratos Multiphysics framework and validated on two benchmark configurations: the 2D NACA 0012 airfoil and the 3D ONERA M6 wing. The resulting ROMs achieve accurate reconstructions of aerodynamic fields and coefficients, with relative errors on the order of 10−3$$ 1{0}^{-3} $$, while reducing the dimensionality of the full order models by approximately three orders of magnitude. Although the corresponding speed‐ups (×2$$ \times 2 $$ in 2D and ×6.5$$ \times 6.5 $$ in 3D) remain modest for the present linear subspace setting, the results highlight the potential of physics‐based intrusive ROMs as reliable surrogates for transonic flows. In the shock‐dominated regimes examined, the proposed intrusive ROM provides more accurate and physically consistent solutions than standard data‐driven surrogates. The framework provides a solid baseline for future extensions incorporating hyper‐reduction and non‐linear ROM strategies. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/nme.70251
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        Text: English
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      – SubjectFull: Transonic flow
        Type: general
      – SubjectFull: Aerodynamics
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      – SubjectFull: Reduced-order models
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      – SubjectFull: Proper orthogonal decomposition
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      – SubjectFull: Shock waves
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      – SubjectFull: Nonlinear analysis
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      – SubjectFull: Computational fluid dynamics
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      – TitleFull: Non‐Linear Reduced Order Modelling of Transonic Potential Flows for Fast Aerodynamic Analysis.
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              Text: 1/30/2026
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