Finite element simulation of a two-dimensional standing wave thermoacoustic engine

Thermoacoustic engines use heat to produce acoustic power. The subject of this manuscript is modeling of thermoacoustic engines. A finite element simulation has been performed on a theoretical example of a two-dimensional standing wave thermoacoustic engine. The simulation solves the linearized Navier-Stokes equations in the frequency domain. The analysis is used to obtain the (thermo)acoustic eigenfrequencies and the corresponding mode shapes of the engine. The nonlinear eigenfrequency problem is solved using an iterative (modified) Newton-Raphson method. The engine starts to oscillate (onset) when a linear instability is present. An instability can be determined when the imaginary part of an eigenfrequency of the engine crosses zero and becomes negativ