Two moment neutrino transport (Cernohorsky & van Weert 1992)
consists in solving the spectral energy and momentum balance equations
as a coupled set.
Let us define the moment of the distribution function
and the following Eddington factors
For the sake of simplicity we will omit the energy dependence. Quantities with bar () will stand for antineutrinos and analogous definitions to (13-16) will be used.
In order to close the set formed by the two equations (energy and momentum) we need two closure relations p=p(f,I0) and q=q(f,I0). In the next section we give some closure relations widely used in the literature.
The source terms in the energy and momentum balance equations are obtained by angular integration of the collision term on the right hand side of the Boltzmann equation
These source terms are the contribution of the TP process to the energy and momentum exchange between neutrinos and matter. After using the Legendre expansion (4) the expression for S0 and S1 can be obtained