In order to improve convergence, a semi-implicit treatment is adopted for the momentum and heat source terms on the CFD side of the coupling. In this procedure, rather than simply using the value of the drag force and convective heat transfer computed in the DEM solver, these terms are divided into an explicit and an implicit part.
To apply this procedure, is rewritten using Equation 2–8 and Equation 3–5:
 | (6–1) |
 | (6–2) |
In this last equation, 
is the momentum exchange coefficient between solid and fluid phase,
defined as:
 | (6–3) |
where 
is the drag coefficient, calculated using the correlations presented in
section Drag force and 
is the area of the particle projected in the force direction.
Since in the classic finite volume method the fluid velocity is considered constant within a cell, the first term on the right hand side of the Equation 6–2 can be subdivided into two terms and written as:
 | (6–4) |
This expression can be further rewritten, splitting the interaction forces into an explicit term, A, and an implicit term, B, that is function of the fluid velocity on the current time step:
 | (6–5) |
The heat exchange between particles and fluid is calculated in Rocky and sent to Fluent via a source term. This source term is linearized to enhance stability on the CFD side of the simulation.
The expression for the heat transfer rate between particle and fluid is:
 | (6–6) |
Equation 6–7 can be split into two terms following the general linearized source term on fluent [44] at section Linearized Source Terms:
 | (6–7) |
Then, the following equivalences arise from the source term linearization:
 | (6–8) |