Nek5000

Stability tools for the spectral-element code Nek5000: application to jet-in-crossflow We demonstrate the use of advanced linear stability tools developed for the spectral-element code Nek5000 to investigate the dynamics of nonlinear flows in moderately complex geometries. The aim of stability calculations is to identify the driving mechanism as well as the region most sensitive to the instability: the wavemaker. We concentrate on global linear stability analysis, which considers the linearised Navier--Stokes equations and searches for growing small disturbances, i.e. so-called linear global modes. In the structural sensitivity analysis these modes are associated to the eigenmodes of the direct and adjoint linearised Navier--Stokes operators, and the wavemaker is defined as the overlap of the strongest direct and adjoint eigenmodes. The large eigenvalue problems are solved using matrix-free methods adopting the time-stepping Arnoldi approach. We present here our implementation in Nek5000 with the ARPACK library on a number of test cases.


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  1. Abreu, Leandra I.; Tanarro, Alvaro; Cavalieri, André V. G.; Schlatter, Philipp; Vinuesa, Ricardo; Hanifi, Ardeshir; Henningson, Dan S.: Spanwise-coherent hydrodynamic waves around flat plates and airfoils (2021)
  2. Brown et al.: libCEED: Fast algebra for high-order element-based discretizations (2021) not zbMATH
  3. Ellingsen, Simen Å.; Akselsen, Andreas H.; Chan, Leon: Designing vortices in pipe flow with topography-driven Langmuir circulation (2021)
  4. Feng, Zhe; Zhang, Mengqi; Vazquez, Pedro A.; Shu, Chang: Deterministic and stochastic bifurcations in two-dimensional electroconvective flows (2021)
  5. Fytanidis, Dimitrios K.; García, Marcelo H.; Fischer, Paul F.: Mean flow structure and velocity-bed shear stress maxima phase difference in smooth wall, transitionally turbulent oscillatory boundary layers: direct numerical simulations (2021)
  6. Guerrero, Byron; Lambert, Martin F.; Chin, Rey C.: Transient dynamics of accelerating turbulent pipe flow (2021)
  7. Kern, J. S.; Beneitez, M.; Hanifi, A.; Henningson, D. S.: Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes (2021)
  8. Loiseau, Jean-Christophe; Brunton, Steven L.; Noack, Bernd R.: From the POD-Galerkin method to sparse manifold models (2021)
  9. Ma, Yuchen; Peltier, W. R.: Parametrization of irreversible diapycnal diffusivity in salt-fingering turbulence using DNS (2021)
  10. Rezaeiravesh, Saleh; Vinuesa, Ricardo; Schlatter, Philipp: On numerical uncertainties in scale-resolving simulations of canonical wall turbulence (2021)
  11. Zaripov, Dinar; Ivashchenko, Vladislav; Mullyadzhanov, Rustam; Li, Renfu; Mikheev, Nikolay; Kähler, Christian J.: On a mechanism of near-wall reverse flow formation in a turbulent duct flow (2021)
  12. Abreu, Leandra I.; Cavalieri, André V. G.; Schlatter, Philipp; Vinuesa, Ricardo; Henningson, Dan S.: Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows (2020)
  13. Blanchard, Antoine; Bergman, Lawrence A.; Vakakis, Alexander F.: Vortex-induced vibration of a linearly sprung cylinder with an internal rotational nonlinear energy sink in turbulent flow (2020)
  14. Chen, Xue; Chung, Yongmann M.; Wan, Minping: Uniform-momentum zones in a turbulent pipe flow (2020)
  15. Le Clainche, Soledad; Vega, José M.: A review on reduced order modeling using DMD-based methods (2020)
  16. Negi, P. S.; Hanifi, A.; Henningson, D. S.: On the linear global stability analysis of rigid-body motion fluid-structure-interaction problems (2020)
  17. Offermans, N.; Peplinski, A.; Marin, O.; Schlatter, P.: Adaptive mesh refinement for steady flows in Nek5000 (2020)
  18. Picella, F.; Robinet, J.-Ch.; Cherubini, S.: On the influence of the modelling of superhydrophobic surfaces on laminar-turbulent transition (2020)
  19. Romanò, Francesco; Türkbay, Tuǧçe; Kuhlmann, Hendrik C.: Lagrangian chaos in steady three-dimensional lid-driven cavity flow (2020)
  20. Sahoo, Swarandeep; Sreenivasan, Binod: Convection in a rapidly rotating cylindrical annulus with laterally varying boundary heat flux (2020)

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