My derivation of the linearization of “Energy dissipation by collision” is different from the one given in mfix code.
There is only the LHS term in the code after the dissipation term is linearized, which is:
But I think for the source term:
it can be linearized as:
in which:
My derivation shows that both LHS and RHS term should exit, but the code only gives a LHS term.
If Qc=-K.theta^(3/2) = -LHS.theta + RHS then a natural choice is LHS=k.theta^(1/2) and RHS=0
Your choice LHS=(3/2)theta^(1/2) and RHS=(1/2)theta^(3/2) works mathematically but RHS still contains theta.
Thank you for your reply. After a deeper study, I’ve learned that there are more than one way of linearization of source term. Many CFD books introduce only one method of linearization as I mentioned in the question, so I was confused. Now, my problem is solved.
