nekStab: open-source toolbox for large-scale stability analysis in Nek5000

Over the past decade, stability analyses of complex three-dimensional flows have become feasible. They moreover provide new insights into the early transition mechanisms. Likewise, computing unstable periodic orbits (UPO) is instrumental in understanding turbulence in canonical flows. Few tools are however available in open-source.

In this talk, we'll introduce nekStab, an open-source and user-friendly toolbox for Nek5000. Based on a matrix-free formulation, it enables users to compute fixed points (resp. UPO) via a Newton-GMRES solver for arbitrarily complex flow configurations. Computation of the eigenvalues and singular values of the Jacobian (resp. monodromy) matrix relies on a time-stepper Krylov-Schur solver. As Nek5000, nekStab relies only on standard libraries like BLAS and LAPACK, making it portable from laptops to HPC facilities. It moreover requires no modification to the Nek5000 code base.

nekStab presently supports the standard Nek5000 capabilities (e.g., incompressible Navier-Stokes + temperature equations). Efforts to include the new Nek5000 RANS solver are currently undertaken.