It doesn't have to be a really detailed explanation, just like which classes of finite difference schemes and stuff you're using, and perhaps some idea why. I'm curious about MHD
What is best, depends on your problem. Most researchers are quite happy with spectral codes (usually for periodic systems), but if you are interested in large amplitude problems, shocks etc., you might prefer SPH-codes. as summarized for instance in:
The Astrophysical Journal, 652: 1306Y1317, 2006 December 1
MULTIDIMENSIONAL MHD SHOCK TESTS OF REGULARIZED SMOOTHED PARTICLE HYDRODYNAMICS