Matrix-free continuation of large thermoacoustic systems

Abstract

To define the safe operating region of a thermoacoustic system, it is critical to find the regions of parameter space where limit cycles exist. Continuation methods allow limit cycles to be numerically found in the time domain, and can track the changes in the limit cycles as the operating condition of the thermoacoustic system changes. Most continuation methods for finding limit cycles are impractical for large thermoacoustic systems, because the computational time and memory required to form the Jacobian matrices is too large. There are thus only a few applications in the literature of continuation methods for thermoacoustic systems, all with low-order models. Matrix-free shooting methods ..