Matrix-free continuation of limit cycles for bifurcation analysis of large thermoacoustic systems

Abstract

In order to define the nonlinear behaviour of a thermoacoustic system, it is important to find the regions of parameter space where limit cycles exist. Continuation methods find limit cycles numerically in the time domain, with no additional assumptions other than those used to form the governing equations. Once the limit cycles are found, these continuation methods track them as the operating condition of the system changes.Most continuation methods are impractical for finding limit cycles in large thermoacoustic systems because the methods require too much computational time and memory. In the literature, there are therefore only a few applications of continuation methods to thermoacoustic..