Long simulation run-times are the eternal nemesis of the numerical modeller: they impact schedules, prolongate sensitivity analyses, and place practical limits on model scale and the ability to perform comprehensive statistical uncertainty quantification. We present recent software developments in accelerating numerical simulations to combat this. These developments have so far been applied to MODFLOW-USG, but may in future also be implemented in other software that uses Newton-Raphson linearisation. The first development is the truncated Newton method, which computes and applies a dynamic residual-based termination criterion to limit the number of linear solution iterations necessary to solve nonlinear problems. The second development is a new port of the entire MODFLOW outer iteration loop to run on NVIDIA GPU devices, including matrix formulation, nonlinear residual reduction and linear solver logic. The two developments may be used together or separately, and we demonstrate significant speedups in simulation run-time through their use – particularly on modern GPU devices.