In this research we focus on the development of a simulation environment to aid in the development of future technologies, one being ultra-efficient tidal generators. These types of theoretical generators rely on orbital energy to produce free energy with the intent of supporting our increasing global consumption rates. The physical problem at the core of our model and research is the interactions of vortices beneath the surface in near shore zones. This thesis focuses on understanding the underlying simulation constraints and implementing a numerical technique called the Fast Multipole Method (FMM) to reduce the computational complexity of the problem. The FMM method allows us to generate solutions within a prescribed level of accuracy. We must leverage existing software solutions in order to efficiently apply linear algebra operators to large data sets within the framework of the numerical technique. Finally, we strive to manage the limitations of current programming standards employed on High Performance Computing (HPC) architectures. We attempt to achieve this by utilizing tools like ScalFMM and StarPU to enable increased scaling of problems within ever increasing heterogeneous processing unit configurations in HPC architectures.