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Eq.(41)(48) are gas dynamic conservative equations.

(41) 

(42) 

(43) 

(44) 

(45) 

(46) 

(47) 

(48) 
This set of equations is a compromise between the other two sets of
equations. It allows strict numerical conservation of mass, momentum and plasma energy,
but no strict conservation of total energy. In low regions, it
poses no difficulty in simulation. At the same time, the gas dynamic conservative equations
can be combined with the full conservative scheme by integrating both energy
equations and using a 'switch'.
Next: Time and space discretization
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