Computational astrophysics - L10 - Intro to magnetohydrodynamics (MHD)

I introduce the basic equations of magnetohydrodynamics, starting with Maxwell's equations. We take the non-relativistic limit and assume a generalised Ohm's law to derive the equations of MHD. Part of my masters/honours course in computational astrophysics here at Monash University in Melbourne, Australia.

[@justinjozokos1699]

I was like, "Did he learn hour to write backwards just for giving lectures on glass??" and then I realized he probably just mirrored the video. Especially given the fact that he's writing left-handed in the video, but right-handed people are more common

[@woodarddarren]

it messed me up to think thru it I felt it was a double backward, writing in reverse and backward

[@nerosmart5926]

great explanations ı was stuck and could not understand the mhd untill see you thanks

[@vishwamohan2512]

Amazing explaination!!!!, This was something, I was looking for so long!! Thankyou :)

[@parisien01001]

Very nice video, thank you very much ! It is very clear and the way it's explained is also really nice !

[@helenaschwartz7794]

I couldn't handle the squeaking marker. I enjoy your teaching style and would watch without the squeaking.

[@stefanopastore3872]

If you assume that the charge density is zero, why in the Lorentz force you do not neglect J?

[@DanielPriceAstro]

this is a good comment, and I actually don't do the derivation from the generalised Ohm's law anymore in lectures because it is too hand-wavy. Everything is clearer if you just start from electrons and ions ... see here for my updated notes: github.com/danieljprice/cca_school

[@shhdeath3337]

Toooo goood explaination .........

[@justintackett2255]

I noticed you left out the heating and cooling terms of the energy equation there at the end, is assuming adiabatic conditions part of the idealization of MHD or is it done just for simplicity/ brevity's sake?

[@DanielPriceAstro]

yes, this is part of the idealisation because if you have Ohmic resistivity or ion-neutral drift (i.e. non-ideal MHD) then you get heating terms in the energy equation. You can obviously add other heating/cooling that has nothing to do with MHD. The assumption of perfect coupling between ions, electrons and neutrals means you are neglecting the irreversible heating terms caused by the decoupling of these species (e.g. resistive heating).

[@mohamednedal]

How can we solve MHD equations numerically? Could you suggest resources/codes?