Exploring the hydrodynamic boundary of a surface by approaching a colloidal sphere and measuring the occurring drag force is a common experimental technique. However, numerous parameters like the wettability and surface roughness influence the result. In experiments, these cannot be separated easily. For a deeper understanding of such surface effects, a tool is required that predicts the influence of different surface properties. In this paper, we present computer simulations based on the lattice Boltzmann method of a sphere submerged in a Newtonian liquid. We show that our method is able to reproduce the theoretical predictions for flat and non-interacting surfaces. In order to provide high-precision simulation results, the influence of finite size effects has to be well controlled. Therefore, we study the influence of the required system size and resolution of the sphere and demonstrate that even moderate computing resources allow the error to be kept below 1%.