Nek5000 swMATH ID: 8064 Software Authors: Peplinski, A.; Schlatter, P.; Fischer, P.F.; Henningson, D.S. Description: 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. Homepage: http://nek5000.mcs.anl.gov/index.php/Main_Page Related Software: Nektar++; SIMSON; FreeFem++; OpenFOAM; Gmsh; p4est; SINDy; ARPACK; CUDA; deal.ii; PETSc; PyFR; GitHub; hypre; METIS; OCCA; Matlab; Exa-Dune; HE-E1GODF; LOCA Cited in: 144 Publications all top 5 Cited by 315 Authors 28 Schlatter, Philipp 19 Henningson, Dan S. 10 Fischer, Paul F. 9 Hanifi, Ardeshir 7 Loiseau, Jean-Christophe 7 Vinuesa, Ricardo 6 Cherubini, Stefania 5 Moxey, David 5 Peplinski, A. 5 Robinet, Jean-Christophe 4 Alfredsson, Per Henrik 4 Appelquist, E. 4 Brunton, Steven L. 4 Canton, Jacopo 4 Ducoin, Antoine 4 Gallaire, François 4 Lingwood, R. J. 3 Balachandar, S. Raja 3 Blanchard, Antoine B. 3 Boukharfane, Radouan 3 Brandt, Luca 3 Dalcín, Lisandro D. 3 Frouzakis, Christos Emmanouil 3 Kronbichler, Martin 3 Marin, Oana 3 Offermans, N. 3 Ohlsson, Johan 3 Örlü, Ramis 3 Parsani, Matteo 3 Peet, Yulia T. 3 Picella, Francesco 3 Shahriari, Nima 3 Sherwin, Spencer J. 3 Siconolfi, Lorenzo 3 Wall, Wolfgang A. 2 Abreu, Leandra I. 2 Auteri, Franco 2 Avellan, François 2 Bergman, Lawrence A. 2 Brion, Vincent 2 Brynjell-Rahkola, Mattias 2 Bucci, Michele Alessandro 2 Camarri, Simone 2 Cantwell, Chris D. 2 Cavalieri, André V. G. 2 Chin, Rey C. 2 De Palma, Pietro 2 De Vincentiis, Luca 2 Del Rey Fernández, David C. 2 Dutta, Som 2 Eskilsson, Claes 2 Farano, Mirko 2 Fehn, Niklas 2 Feng, Zhe 2 Guerrero, Byron 2 Jacquin, Laurent 2 Keyes, David Elliot 2 Kirby, Robert M. II 2 Lambert, Martin Francis 2 Le Clainche, Soledad 2 Ma, Yuchen 2 Malm, Johan 2 Mantzaras, John 2 Mengaldo, Gianmarco 2 Merzari, Elia 2 Mittal, Ketan 2 Noack, Bernd R. 2 Nolasco, Irving Reyna 2 Pasche, Simon 2 Peltier, W. R. 2 Pizza, Gianmarco 2 Rezaeiravesh, Saleh 2 Salvetti, Maria Vittoria 2 Schrader, Lars-Uve 2 Tanarro, Alvaro 2 Theofilis, Vassilios 2 Tuckerman, Laurette Stephanie 2 Vakakis, Alexander F. 2 van der Poel, Erwin P. 2 Zhang, Mengqi 1 Abdelsamie, Abouelmagd 1 Abide, Stéphane 1 Adrian, Ronald J. 1 Aithal, Abhiram B. 1 Akselsen, Andreas H. 1 Al Jahdali, R. 1 Amici, Roman 1 Amitay, Michael 1 An, Chenge 1 Andriano, C. 1 Anitescu, Mihai 1 Arratia, Cristobal 1 Astolfi, Jacques André 1 Attili, Antonio 1 Bailey, Sean C. C. 1 Battista, Francesco 1 Beck, Andrea D. 1 Bello-Maldonado, Pedro D. 1 Beneitez, Miguel 1 Bengana, Yacine ...and 215 more Authors all top 5 Cited in 24 Serials 68 Journal of Fluid Mechanics 17 Journal of Computational Physics 13 Computers and Fluids 8 European Journal of Mechanics. B. Fluids 3 Computers & Mathematics with Applications 3 Journal of Scientific Computing 3 SIAM Journal on Scientific Computing 2 Acta Mechanica 2 Computer Methods in Applied Mechanics and Engineering 2 Nonlinear Dynamics 2 Combustion Theory and Modelling 2 Communications in Computational Physics 1 Computer Physics Communications 1 Geophysical and Astrophysical Fluid Dynamics 1 International Journal of Computer Mathematics 1 SIAM Review 1 International Journal of Computational Fluid Dynamics 1 Chaos 1 Lobachevskii Journal of Mathematics 1 Journal of Turbulence 1 Matematicheskoe Modelirovanie 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 SIAM Journal on Applied Dynamical Systems 1 Algorithms all top 5 Cited in 17 Fields 132 Fluid mechanics (76-XX) 34 Numerical analysis (65-XX) 9 Partial differential equations (35-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Classical thermodynamics, heat transfer (80-XX) 3 Computer science (68-XX) 3 Mechanics of deformable solids (74-XX) 2 Mechanics of particles and systems (70-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Approximations and expansions (41-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) Citations by Year