Thermoacoustic instability is of fundamental and applied interest in both scientific research and practical applications. This study aims to explore several very important sub-aspects in this field and contribute to a better understanding of thermoacoustic instability as encountered in typical gas turbines and rocket engines. Atomization has been recognized as a key mechanism in driving applied thermoacoustic instability. In this regard, this study mainly focuses on the atomization process relevant for delineation of thermoacoustic instability, contributing to a comprehensive understanding of the effect of acoustics on primary and secondary atomization. Firstly, a tree-based adaptive solver and VOF method are employed to simulate the jet primary atomization. The code is validated by theoretical, numerical and experimental results to demonstrate its capability and accuracy in terms of atomization in both low-speed and high-speed regime. Perturbation frequency and amplitude have shown to affect the atomization significantly. Besides, the effect of acoustic forcing on liquid ligament has also been numerically investigated. A volume source term is introduced to extend the solver to model the compressible effects in the presence of acoustic forcing. The influence of acoustic wave number, amplitude and frequency has been examined in detail. In terms of modelling the thermoacoustic instability, bifurcation analysis is carried out for a time-delayed thermoacoustic system using the Method of Line approach. Good predictions have been obtained to capture the nonlinear behaviors inherent in the system. Moreover, model-based simulation and control of thermoacoustic instability have been conducted. A low-order wave-based network model for acoustics is coupled with nonlinear flame describing function to predict the nonlinear instability characteristics in both frequency and time domain. Furthermore, active feedback control is implemented. Two different controllers have been designed to eliminate the thermoacoustic instability to an acceptably low level and may be employed in a practical manner.