The assessment and mitigation of volcanic risk is mainly related to our ability to derive key eruptive source parameters in real time. Low-frequency acoustic signal generated by explosive eruptions is considered one of the most promising techniques to provide this information in real-time from remote stations. However, a better knowledge of the relationship between the source of volcano infrasound and the volcanic fluid dynamics is still required. In this thesis, the Lattice Boltzmann method (LBM) is investigated as a powerful computational tool to study volcano aeroacoustic source processes. This includes the development and validation of an optimized LBM for aeroacoustic computations, its application to study the generation of acoustic transients by moderate discrete explosive events and the evaluation of a hybrid LBM approach, which can be used to better understand the role of key aspects, e.g. temperature and particle loading, on the source of acoustic signals in volcanic explosive eruptions.