The complexity mainly arises due to the presence of a magnetic field and its coupling with the fluid. One of the important issues is to numerically maintain the  (conservation of magnetic flux) condition, from Maxwell's equations, to avoid the presence of unrealistic effects, namely magnetic monopoles, in the solutions.
The complexity arises primarily due to the interplay between a magnetic field and the surrounding fluid. One key challenge is ensuring that numerical methods preserve the conservation of magnetic flux as dictated by Maxwell's equations, thereby avoiding the introduction of unrealistic effects such as magnetic monopoles.