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.

翻译：封闭燃烧装置（如燃气轮机和火箭）容易发生热声不稳定性。工业设计工程师需要能够在设计周期早期准确识别并消除不稳定性的工具。多年来，研究人员已开发出多种不同方法。本研究聚焦于基于亥姆霍兹波动方程的求解器，该求解器在多数应用中表现出相对快速和准确的特点。该求解器已在许多前期工作中得到研究。频域中的亥姆霍兹波动方程可简化为非线性特征值问题，需要通过求解该问题来计算声模态。先前大多数该求解器的实现依赖线性化求解器和迭代方法，但本研究证明这些方法效率不高且有时不准确。在本研究中，我们利用SLEPc中实现的专用算法，这些算法对非线性特征值问题的特征值计算既准确又高效。我们采用n-tau模型计算亥姆霍兹方程中的反应源项，并描述了推导亥姆霍兹特征值方程以及使用SLEPc库求解该方程所涉及的步骤。