Fluid simulations solving the hydrodynamic (HD) or the magneto-hydrodynamic (MHD) equations are very useful in physics, the latter being particularly useful for modeling plasmas.
Of course these equations are highly nonlinear and solving them accurately is difficult. My first question is, in the general case what some specific numerical challenges for building good fluid simulations solving HD/MHD?
I am also interested in the specific case of modeling multiphase gases, like those that appear in galaxy halos. What are the specific numerical challenges in this case?