When drilling a geothermal wellbore, hard and abrasive rock types, such as granite, are encountered. Therefore, the rate of penetration (ROP) decreases, which has a substantial impact on drilling costs. A possible approach to increase ROP is the development and application of a jet-assisted drilling system. This work is focused on different types of numerical simulations, which are used to support the development of this drilling system. First, the mechanics of a submerged jet impinging on a solid surface are considered and a basic CFD simulation study including the pressure and velocity distributions in the regions of interest is conducted. Moreover, full three-dimensional simulations of a conventiontal roller cone bit incorporating a high-pressure nozzle are conducted, whereas the nozzle inclination angle, the bit rotational speed and the nozzle geometry are varied. As a next step, the jet-rock interaction is investigated by three different numerical approaches: a coupled CFD-FEM approach, Smoothed Particle Hydrodynamics (SPH) and Coupled Eulerian-Lagrangian (CEL). For atmospheric conditions, the SPH and CEL simulations are carried out by using exactly the same boundary conditions. The obtained stress distributions and the cutting performance in the impingement region of the jet are compared to each other and the corresponding conclusions are drawn. Moreover, SPH simulations at downhole conditions are carried out and evaluated. In the last part of this work the effect of a jetted kerf on drilling performance is investigated. To this end a so-called undamaged wellbore model and a pre-jetted one are created, which both contain a rigid cone that includes a single cutter element only. Before the cone is rotated, the hydrostatic pressure in the borehole, the corresponding wellbore stresses and sufficient weight on bit are applied. Finally, the distribution of the degradation of the rock elements' elastic stiffness is evaluated in the impact zone of the cutting element and the results of the two wellbore models are compared. Thus, a statement regarding the effect of a jet-assisted drilling system on ROP can be made.