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. Al Jahdali, R.; Dalcin, L.; Boukharfane, R.; Nolasco, I. R.; Keyes, D. E.; Parsani, M.: Optimized explicit Runge-Kutta schemes for high-order collocated discontinuous Galerkin methods for compressible fluid dynamics (2022)
  2. Burtsev, Anton; He, Wei; Zhang, Kai; Theofilis, Vassilios; Taira, Kunihiko; Amitay, Michael: Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers (2022)
  3. Callaham, Jared L.; Brunton, Steven L.; Loiseau, Jean-Christophe: On the role of nonlinear correlations in reduced-order modelling (2022)
  4. Camarri, Simone: T-shaped micromixers aligned in a row: characterization of the engulfment regime (2022)
  5. De Vincentiis, Luca; Henningson, Dan S.; Hanifi, Ardeshir: Transition in an infinite swept-wing boundary layer subject to surface roughness and free-stream turbulence (2022)
  6. Ganju, Sparsh; Bailey, Sean C. C.; Brehm, Christoph: Amplitude and wavelength scaling of sinusoidal roughness effects in turbulent channel flow at fixed (Re_\tau= 720) (2022)
  7. Jaiswal, Shashank: Non-linear Boltzmann equation on hybrid-unstructured non-conforming multi-domains (2022)
  8. Jiang, Hao-Kui; Luo, Kang; Zhang, Zi-Yao; Wu, Jian; Yi, Hong-Liang: Global linear instability analysis of thermal convective flow using the linearized lattice Boltzmann method (2022)
  9. Keeton, Benjamin W.; Carpio, Jaime; Nomura, Keiko K.; Sánchez, Antonio L.; Williams, Forman A.: Vortex breakdown in variable-density gaseous swirling jets (2022)
  10. Lengani, D.; Simoni, D.; Pralits, J. O.; Đurović, K.; De Vincentiis, L.; Henningson, D. S.; Hanifi, A.: On the receptivity of low-pressure turbine blades to external disturbances (2022)
  11. Lloyd, C. J.; Dorrell, R. M.; Caulfield, C. P.: The coupled dynamics of internal waves and hairpin vortices in stratified plane Poiseuille flow (2022)
  12. Ma, Yuchen; Peltier, W. R.: Diapycnal diffusivities in Kelvin-Helmholtz engendered turbulent mixing: the diffusive-convection regime in the arctic ocean (2022)
  13. Morita, Y.; Rezaeiravesh, S.; Tabatabaei, N.; Vinuesa, R.; Fukagata, K.; Schlatter, P.: Applying Bayesian optimization with Gaussian process regression to computational fluid dynamics problems (2022)
  14. Mukherjee, S.; Paul, M. R.: The fluid dynamics of propagating fronts with solutal and thermal coupling (2022)
  15. Nobis, Harrison; Schlatter, Philipp; Wadbro, Eddie; Berggren, Martin; Henningson, Dan S.: Topology optimization of unsteady flows using the spectral element method (2022)
  16. Yang, Yongliang; Feng, Zhe; Zhang, Mengqi: Onset of vortex shedding around a short cylinder (2022)
  17. Abdelsamie, Abouelmagd; Lartigue, Ghislain; Frouzakis, Christos E.; Thévenin, Dominique: The Taylor-Green vortex as a benchmark for high-fidelity combustion simulations using low-Mach solvers (2021)
  18. 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)
  19. Bongarzone, Alessandro; Bertsch, Arnaud; Renaud, Philippe; Gallaire, François: Impinging planar jets: hysteretic behaviour and origin of the self-sustained oscillations (2021)
  20. Brown et al.: libCEED: Fast algebra for high-order element-based discretizations (2021) not zbMATH

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