Hydrokinetic flapping foil turbines in swing-arm mode have gained considerable interest in recent years because of their enhanced capability to extract power, and improved efficiency compared to foils in simple mode. The performance of foil turbines is closely linked to the development and separation of the leading-edge vortex (LEV). The paper's aim is to develop a purpose-built 2D numerical model to present the capability of integrating the weighted residual finite element method (FEM) with the interface capturing technique, level-set method (LSM), in providing a high-quality numerical simulation of the flapping foil in swing-arm mode, by accurately modeling the formation and the separation of the LEV on flapping foils. The solvers were validated against well-known static and dynamic benchmark problems and the effect of the mesh density was analyzed and discussed. This paper further covers an initial investigation of the hydrodynamics of flapping foil in swing-arm mode, by studying the structure of the vortex around a NACA0012 foil. The presented method helps to provide a better understanding of the relation between the Leading-Edge Vortex creation, growth, and separation over the flapping foil in swing-arm mode and the extracted power from a hydrokinetic turbine.