The evaluation of forces acting on marine structures and modelling the complex fluid-body interaction of floating structures is crucial in marine engineering. While current CFD models based on the Navier-Stokes equation are able to represent the behaviour of floating bodies with great accuracy, fully non-linear potential flow solvers are able to model realistic extreme sea states at a fraction of usual computational costs. A Finite Difference based fully non-linear potential flow model with the ability to represent complex fluid-structure interaction and floating, would therefore be a major advantage for the design of marine structures. The first step is hereby the solver itself. Therefore the fully non-linear potential flow model REEF3D::PTF is developed, using a Finite Differences Scheme. A level set function is used for free surface representation and an immersed boundary method is used to enforce boundary conditions. The free surface potential and location are advanced in time, while the potential field is gained from solving the Laplace Equation. Different numerical methods for solving the Laplace Equation at the free surface are developed, implemented and tested. Comparison, to analytical values, experimental data and the σ-grid solver REEF3D::FNPF show a high sensibility of the fixed grid solver REEF3D::PTF regarding the used free surface treatment method in the Laplace Equation. Since this sensibility is found to be the main reason for small remaining inaccuracies, the fixed grid model PTF shows to have great potential to be further perfected and suitable for future implementation of complex structures and floating bodies. Thus, the future work will focus on addressing this sensitivity and optimise the free surface treatment for improved accuracy and reliability.