High resolution scale-resolving simulations have recently received more interest due to the increase in available computational power. For such simulations, high-order accurate schemes have significant benefits since they are much less subjected to numerical error and therefore less likely to suppress flow instabilities, but they also present new challenges and issues to be aware of compared to more traditional ones. In particular, the numerical interpolation around sharp discontinuities may be a source of instabilities and numerical oscillations, which can lead to non-physical results, such as negative density, pressure or temperature, and cause the simulation to crash. In this work different strategies and methods are presented to stabilise a high-resolution simulation of non-neutral plasmas subjected to a magnetic field - such as also encountered in HET -, the canonical Penning discharge case study characterized by expansion into a vacuum at the boundary.