  Closed combustion devices like gas turbines and rockets are prone to
thermoacoustic instabilities. Design engineers in the industry need tools to
accurately identify and remove instabilities early in the design cycle. Many
different approaches have been developed by the researchers over the years. In
this work we focus on the Helmholtz wave equation based solver which is found
to be relatively fast and accurate for most applications. This solver has been
a subject of study in many previous works. The Helmholtz wave equation in
frequency space reduces to a nonlinear eigenvalue problem which needs to be
solved to compute the acoustic modes. Most previous implementations of this
solver have relied on linearized solvers and iterative methods which as shown
in this work are not very efficient and sometimes inaccurate. In this work we
make use of specialized algorithms implemented in SLEPc that are accurate and
efficient for computing eigenvalues of nonlinear eigenvalue problems. We make
use of the n-tau model to compute the reacting source terms in the Helmholtz
equation and describe the steps involved in deriving the Helmholtz eigenvalue
equation and obtaining its solution using the SLEPc library.
