Convective terms

Equation (604) is still valid. For incompressible fluids the Gamma method is applied which results in (Equation (577)):

$\displaystyle \overrightarrow{\boldsymbol{v}}_f ^{(m-1)} = \gamma \overline{\bo...
...bol{v} }_f ^{(m-1)} + (1-\gamma) \overrightarrow{\boldsymbol{v} }_f ^{UD(m-1)}.$ (760)

Therefore, one ends up with:

$\displaystyle (A) \approx \sum_{f}^{} \dot{m}_f^{(m-1)} A_f \left[\overrightarr...
...\overline{(v_i)}_f^{(m-1)}-\overrightarrow{(v_i)}_f^{UD(m-1)} \right ) \right].$ (761)