Volume forces

The term with volume forces is modeled by:

\int_{V}^{} \rho g_i dv \approx \rho_P^{(m-1)} g_i V_P (634)

and ends up on the right hand side.

After solving the resulting system of equations leading to \boldsymbol{v}^{\text{momentum}} the solution \boldsymbol{v}^* is calculated by blending \boldsymbol{v} ^{(m-1)} (20 %) with \boldsymbol{v}^{\text{momentum}} (80 %). This is called underrelaxation and is needed to ensure stability in the SIMPLE scheme (the specifics of this scheme will be discussed when treating the conservation of mass). For the SIMPLE scheme underrelaxation is needed for all conservation equations: for the conservation of momentum, temperature, k and \omega in the above blend, for the conservation of mass using the inverse blend, i.e. 20 % of the new solution combined with 80 % of the old solution. For the SIMPLEC scheme (also discussed further along the line) no underrelaxation is needed.