Steffen Schotthöfer, TU Kaiserslautern
Sensitivity analysis in the presence of limit cycle oscillations – Regularizing methods
Many unsteady problems equilibrate to periodic behavior. For these problems the sensitivity of periodic outputs to system parameters are often desired and must be estimated from a finite time span. Sensitivities computed in the time domain over a finite time span can take excessive time to converge or fail to do so. In this presentation two approaches will be discussed to overcome these difficulties.
First, the so called windowing approach uses weighting functions to improve convergence behavior. We will consider long-time and short-time windowing as two aspects of this approach. The idea of a long time window is to average over a big, non-integer number of periods of the weighted output, to archive convergence. On the other hand, the idea of short time windowing is to average over a small, integer multiple of a period. Convergence is archived by refining the period approximation.
Second, an analytic approach is discussed. Here we set up an additional boundary value problem to exactly compute the influence of parameter changes on amplitude, period and relative phase.
We will discuss the efficiency of both approaches and their usability in SU2 and aerodynamic applications.