Time-stepping global stability analysis using open-source DNS and DSMC codes

On occasion TriGlobal linear stability analysis is prohibitively expensive within a matrix-forming paradigm due to its very high memory requirement. Moreover, a matrix-based approach is inapplicable to rarefied flows encountered at high altitudes, where one resorts to particle-based numerical simulations. In such situations, global stability analysis can be performed using matrix-free, time-stepping approaches recovering flow eigenmodes directly from nonlinear solvers, while preserving all underlying assumptions with additional advantage of drastic reduction in memory requirements.

Our current work combines a time-stepping algorithm with compressible, open-source solvers, both in a continuum (rhoCentralFoam and rhoPimpleFoam) and a kinetic theory (dsmcFoam and SPARTA) context. Compressible Couette and 3D open cavity flows have been used as validation cases. We find that the order of the computational stencil used for Jacobian approximation by Frechet derivatives has a significant impact on the error of eigenfunctions near supersonic boundaries while eigenvalues remained weakly affected in the cases considered. Work continues to uncover global flow eigenmodes over 3D configurations in both continuum and rarefied flow regimes at super/hypersonic flow conditions.