Collision terms for integer moments

For the special case in which q = l2 = is = 0, we define = 0. Note that in this definition for the magnitude of g appears to the power i + 2. This is done so that 

We can now express the collision source term and collisional-flux term for the integer moments of order y as 

the four contributions on the right-hand side are defined as  

Note that, using the result in Eq. (6.107), we can rewrite Eq. (6.105) more compactly as 

In Section 6.4, we will apply these results to And the moment-tfansport equations for a 

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For quadrature-based moment methods, the collision terms for integer moments are needed. For this special case, the method developed in Fox Vedula (2010) leads to closed expressions for the integrals in terms of finite sums. For integer moments, we have il/ y) = Vj 2 Vg and the terms in the sums over n in Eqs. (6.55)-(6.57) are zero for n > max(/i, /2. h)- For this particular case, we will define for m = 0 by... 

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