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. Capuano, Francesco; Palumbo, Andrea; de Luca, Luigi: Comparative study of spectral-element and finite-volume solvers for direct numerical simulation of synthetic jets (2019)
  2. Ducoin, A.; Astolfi, J. A.: Wall-pressure fluctuations of laminar separation bubble based on direct numerical simulation and experiments over a hydrofoil at (\mathrmRe=450,000) (2019)
  3. Abide, Stéphane; Viazzo, Stéphane; Raspo, Isabelle; Randriamampianina, Anthony: Higher-order compact scheme for high-performance computing of stratified rotating flows (2018)
  4. Appelquist, E.; Schlatter, P.; Alfredsson, P. H.; Lingwood, R. J.: Turbulence in the rotating-disk boundary layer investigated through direct numerical simulations (2018)
  5. Farano, M.; Cherubini, S.; De Palma, P.; Robinet, J.-C.: Nonlinear optimal large-scale structures in turbulent channel flow (2018)
  6. Kooij, Gijs L.; Botchev, Mikhail A.; Frederix, Edo M. A.; Geurts, Bernard J.; Horn, Susanne; Lohse, Detlef; van der Poel, Erwin P.; Shishkina, Olga; Stevens, Richard J. A. M.; Verzicco, Roberto: Comparison of computational codes for direct numerical simulations of turbulent Rayleigh-Bénard convection (2018)
  7. Méndez, M.; Shadloo, M. S.; Hadjadj, A.; Ducoin, A.: Boundary layer transition over a concave surface caused by centrifugal instabilities (2018)
  8. Minjeaud, Sebastian; Pasquetti, Richard: High order (C^0)-continuous Galerkin schemes for high order PDEs, conservation of quadratic invariants and application to the Korteweg-de Vries model (2018)
  9. Sharma, S.; Ducoin, A.: Direct numerical simulation of the effect of inlet isotropic turbulence on centrifugal instabilities over a curved wall (2018)
  10. Pitton, Giuseppe; Rozza, Gianluigi: On the application of reduced basis methods to bifurcation problems in incompressible fluid dynamics (2017)
  11. Appelquist, E.; Imayama, Shintaro; Alfredsson, P. Henrik; Schlatter, P.; Lingwood, R. J.: Linear disturbances in the rotating-disk flow: a comparison between results from simulations, experiments and theory (2016)
  12. Ducoin, A.; Loiseau, J.-C.; Robinet, J.-C.: Numerical investigation of the interaction between laminar to turbulent transition and the wake of an airfoil (2016)
  13. Siconolfi, L.; Fani, A.; Camarri, S.; Salvetti, M. V.: Effect of geometry modifications on the engulfment in micromixers: numerical simulations and stability analysis (2016)
  14. Cantwell, C. D.; Moxey, D.; Comerford, A.; Bolis, A.; Rocco, G.; Mengaldo, G.; De Grazia, D.; Yakovlev, S.; Lombard, J.-E.; Ekelschot, D.; Jordi, B.; Xu, H.; Mohamied, Y.; Eskilsson, C.; Nelson, B.; Vos, P.; Biotto, C.; Kirby, R. M.; Sherwin, S. J.: Nektar++: an open-source spectral/(hp) element framework (2015)
  15. Peplinski, A.; Schlatter, P.; Henningson, D. S.: Global stability and optimal perturbation for a jet in cross-flow (2015)
  16. Peplinski, A.; Schlatter, P.; Fischer, P. F.; Henningson, D. S.: Stability tools for the spectral-element code Nek5000: application to jet-in-crossflow (2014)
  17. Roderick, Oleg; Anitescu, Mihai; Peet, Yulia: Proper orthogonal decompositions in multifidelity uncertainty quantification of complex simulation models (2014)
  18. Borrell, Guillem; Sillero, Juan A.; Jiménez, Javier: A code for direct numerical simulation of turbulent boundary layers at high Reynolds numbers in BG/P supercomputers (2013)
  19. Malm, Johan; Schlatter, Philipp; Fischer, Paul F.; Henningson, Dan S.: Stabilization of the spectral element method in convection dominated flows by recovery of skew-symmetry (2013)
  20. Malm, Johan; Schlatter, Philipp; Henningson, Dan S.: Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser (2012)

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