Time-Resolved Adaptive Direct FEM Simulation of High-Lift Aircraft Configurations

  • Johan JanssonEmail author
  • Ezhilmathi Krishnasamy
  • Massimiliano Leoni
  • Niclas Jansson
  • Johan Hoffman


We present an adaptive finite element method for time-resolved simulation of aerodynamics without any turbulence-model parameters, which is applied to a benchmark problem from the HiLiftPW-3 workshop to compute the flow past a JAXA Standard Model (JSM) aircraft model at realistic Reynolds numbers. The mesh is automatically constructed by the method as part of an adaptive algorithm based on a posteriori error estimation using adjoint techniques. No explicit turbulence model is used, and the effect of unresolved turbulent boundary layers is modeled by a simple parametrization of the wall shear stress in terms of a skin friction. In the case of very high Reynolds numbers, we approximate the small skin friction by zero skin friction, corresponding to a free-slip boundary condition, which results in a computational model without any model parameter to be tuned, and without the need for costly boundary-layer resolution. We introduce a numerical tripping-noise term to act as a seed for growth of perturbations; the results support that this triggers the correct physical separation at stall and has no significant pre-stall effect. We show that the methodology quantitavely and qualitatively captures the main features of the JSM experiment—aerodynamic forces and the stall mechanism—with a much coarser mesh resolution and lower computational cost than the state-of-the-art methods in the field, with convergence under mesh refinement by the adaptive method. Thus, the simulation methodology appears to be a possible answer to the challenge of reliably predicting turbulent-separated flows for a complete air vehicle.



lift coefficient (dimensionless)


drag coefficient (dimensionless)


pressure coefficient (dimensionless)


diameter of tetrahedron in finite element mesh (m)


time step (s)

\(\mathbf {n}\)

normal unit vector (dimensionless)


computed pressure (Pa)


pressure (Pa)


pressure test function (Pa)


Reynolds number (dimensionless)


time variable (s)


end time (s)

\(\mathbf {U}\)

computed velocity (\({\mathrm{m}\,\mathrm{s}^{-1}}\))

\(\mathbf {u}\)

velocity (\({\mathrm{m}\,\mathrm{s}^{-1}}\))

\(\mathbf {v}\)

velocity test function (\({\mathrm{m}\,\mathrm{s}^{-1}}\))

\(\mathbf {x}\)

space variable (m)

\(\alpha \)

angle of attack (dimensionless)

\(\beta \)

friction parameter (\({\mathrm{kg}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}}\))

\(\nu \)

kinematic viscosity (\({\mathrm{m}^{2}\,\mathrm{s}^{-1}}\))

\(\mathbf {\tau }\)

tangent unit vector (dimensionless)



This research has been supported by the European Research Council, the H2020 MSO4SC grant, the Swedish Research Council, the Swedish Foundation for Strategic Research, the Swedish Energy Agency, the Basque Excellence Research Center (BERC 2014–2017) program and ELKARTEK GENTALVE project by the Basque Government, the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa accreditation SEV-2013-0323 and the Project of the Spanish Ministry of Economy and Competitiveness with reference MTM2013–40824 and La Caixa. We acknowledge the Swedish National Infrastructure for Computing (SNIC) at PDC—Center for High-Performance Computing for granting us access to the supercomputer resources Beskow.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Johan Jansson
    • 1
    • 2
    Email author
  • Ezhilmathi Krishnasamy
    • 1
    • 2
  • Massimiliano Leoni
    • 1
    • 2
  • Niclas Jansson
    • 1
  • Johan Hoffman
    • 1
  1. 1.Computational Science and Technology CSC, KTHStockholmSweden
  2. 2.BCAM - Basque Center for Applied MathematicsBilbaoSpain

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