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Current experimental methods are not able to determine the mobility of flat grain boundaries across the large misorientation phase space. We find that the synthetic driving force method proposed to achieve this feat by simulation has a deficiency concerning numerical accuracy. We introduce a new synthetic driving force method by defining a new way to differentiate between crystal orientations. In contrast to the former method, this has the advantage that energy is correctly preserved during the simulation and is thus more reliable. This also results in a closer match of the applied energy difference to the thermodynamic free energy. This reduces the necessity of a post-simulation correction of the applied energy per atom to resulting driving pressure. We compare the newly proposed version to the old one for two grain boundaries and investigate the influence of simulation parameters on the resulting mobility values. For future simulations using a synthetic grain boundary driving force, we recommend using this newly proposed version over previous methods.