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 intricacy arises mainly due to the coexistence of a magnetic field and its interaction with the fluid. A crucial issue is maintaining numerically the (conservation of magnetic flux) condition from Maxwell's equations to avoid the presence of implausible effects, namely magnetic monopoles, in the solutions.