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. 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)
  2. 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)
  3. Pitton, Giuseppe; Rozza, Gianluigi: On the application of reduced basis methods to bifurcation problems in incompressible fluid dynamics (2017)
  4. 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)
  5. Peplinski, A.; Schlatter, P.; Fischer, P. F.; Henningson, D. S.: Stability tools for the spectral-element code Nek5000: application to jet-in-crossflow (2014)
  6. Roderick, Oleg; Anitescu, Mihai; Peet, Yulia: Proper orthogonal decompositions in multifidelity uncertainty quantification of complex simulation models (2014)
  7. 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)
  8. 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)
  9. Malm, Johan; Schlatter, Philipp; Henningson, Dan S.: Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser (2012)
  10. Pizza, Gianmarco; Frouzakis, Christos E.; Mantzaras, John: Chaotic dynamics in premixed hydrogen/air channel flow combustion (2012)
  11. Tempelmann, David; Hanifi, Ardeshir; Henningson, Dan S.: Spatial optimal growth in three-dimensional compressible boundary layers (2012)
  12. Ohlsson, J.; Schlatter, P.; Fischer, P. F.; Henningson, D. S.: Stabilization of the spectral-element method in turbulent flow simulations (2011)
  13. Ohlsson, J.; Schlatter, P.; Mavriplis, C.; Henningson, D. S.: The spectral-element and pseudo-spectral methods: a comparative study (2011)
  14. Schrader, Lars-Uve; Brandt, Luca; Zaki, Tamer A.: Receptivity, instability and breakdown of Görtler flow (2011)
  15. Schwänen, Markus; Duggleby, Andrew: Optimizing turbulent heat transfer using orthogonal decomposition-based contouring (2011)
  16. Ohlsson, Johan; Schlatter, Philipp; Fischer, Paul F.; Henningson, Dan S.: Direct numerical simulation of separated flow in a three-dimensional diffuser (2010)
  17. Pizza, G.; Frouzakis, C. E.; Mantzaras, J.; Tomboulides, A. G.; Boulouchos, K.: Three-dimensional simulations of premixed hydrogen/air flames in microtubes (2010)
  18. Schrader, L.-U.; Brandt, L.; Mavriplis, C.; Henningson, D. S.: Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge (2010)