Optimization, Stability and Sensitivity

On the stability analysis of compressible and turbulent Navier-Stokes flows, a smart and efficient use of computational and human resources is an asset. NUMATH team has integrated a number of public libraries (PETSc, SLEPc, MUMPS, among others) into zTAUev, an in-house code that permits the calculation of the associated large scale eigenvalue problem.

Based on a discrete formulation (first-discretize-then-linearize), it allows to extract the so-called global modes of the flow system, namely the perturbations that may grow in time and space and generate non-symmetrical or unsteady configurations.

Moreover, by means of the use of a discrete-adjoint approach, the developed tool computes the sensitivity of the least stable eigenvalue to external perturbations, obtaining not only the core location of the instability, but also its sensitivity to the application of a source of local forcing or heating/cooling.

Ultimately, it is possible to obtain the effects that localised surface deformation will have on the eigenvalue associated to the global instability.