Underwater radiated noise from shipping activities and offshore wind turbine construction acts as a stressor for marine mammals. Thus, there is an urgent need to develop accurate underwater noise prediction capability to regulate industrial marine activities. Existing practices for routine numerical modelling of underwater ocean noise still rely on hybrid numerical-analytical techniques like numerical ray or beam tracing, which suffer from numerical artefacts like caustics and shadow zones in the computational domain. Furthermore, they cannot be employed for analysing underwater acoustics in the presence of complex ocean bathymetries and arbitrary acoustic sources. This motivates the development of more accurate computational models, which can capture the multiphysics nature of underwater ocean acoustics. This research will present some of the early computational modelling efforts of underwater ocean acoustic propagation using a high-order spectral element solver of the acoustic perturbation equation via an open-source code Nektar++. Preliminary studies have demonstrated that the acoustic perturbation solver can capture the physics of acoustic scattering and mixed boundary conditions can be accurately modelled. Furthermore, the far-field acoustic transmission loss in the underwater ocean domain over large distances due to geometric spreading and acoustic scattering from two-dimensional seamount structures have been validated against finite-element beam tracing methods. The results presented below show promise for expanding the current computational modelling approach to three-dimensional domains and coupled fluid-acoustic modelling. These will be presented in the final paper.