Convection term

$\displaystyle \int_{A}^{} c_v T \rho \boldsymbol{v} \cdot \boldsymbol{n} da \approx \sum_{f}^{} \dot{m} _f ^{(m)} c_v ^{(m-1)} \overrightarrow{T}_f ^{(m)}.$ (700)

Notice that the corrected mass flow (calculated in iteration $ (m)$) is taken! $ \overrightarrow{T}_f ^{(m)}$ is approximated by (cf. the exposure in the section on the conservation of momentum):

$\displaystyle \overrightarrow{T}_f ^{(m)} \approx \overrightarrow{T}_f ^{UD(m)}...
...left [ \overrightarrow{T}_f ^{(m-1)} - \overrightarrow{T}_f^{UD(m-1)} \right ].$ (701)

The boundary conditions amount to:

For the convective interpolation of $ T$ the modified smart algorithm has not shown any advantages, therefore, the upwind difference scheme is always used.