I am trying to implement gas dynamics equations to describe the air heating and expansion due to the passage of the electrical current through the stem’s cross section.
The equation (1) accounts for mass transport.
The equation (2) describes the transport of momentum.
Equations (3) and (4) describe the energy transport.
Here’s the link for a full description: http://membership.agu.org/files/2014/01/da-Silva-and-Pasko-2013-Dynamics-of-streamer-to-leader-transition-at-reduced-air-densities-and-its-implications-for-propagation-of-lightning-leaders-and-gigantic-jets.pdf
I couldn’t find similar topics and I’m struggling to find weak forms for these equations and to implement the model.
May anyone help me with this?