%INTEGRATION_FS_DIRECT%

surface integration of a scalar value along the free surface

INTEGRATION($IntInd$) = ( %INTEGRATION_FS_DIRECT%, ExpressionOfIntegrand, $MaterialTag$ )

The material flag $MaterialTag$ defines the integration area (analogous to the POSTPROCESS-flags for %INTEGRATION_BND_DIRECT%). This computes the integral of a functional $ f$ (ExpressionOfIntegrand) with respect to the free surface $ \partial\Omega_\text{FS}$ identified by the material flag

\begin{align} I_\text{FSDirect} = \int\limits_{\partial\Omega_\text{FS}} f dA\end{align}

by a sum approximation

\begin{align} I_\text{FSDirect} \approx \sum_{i \in P_\text{FS}} f_i \cdot A_i,\end{align}

where $ P_\text{FS}$ is the set of all free surface points with the given material flag and $ A_i$ is the area of the i-th point. Note: Analogous to %INTEGRATION_INT%, a list of material flags can be used to specify the integration area. The number of flags is not limited. Example:

INTEGRATION($IntInd1$) = ( %INTEGRATION_FS_DIRECT%, [Y%ind_p%+Y%ind_p_dyn%], $MaterialTag$ ) INTEGRATION($IntInd2$) = ( %INTEGRATION_FS_DIRECT%, equn{$EqnName$}, $MaterialTag1$, $MaterialTag2$, $MaterialTag3$ ) INTEGRATION($IntInd3$) = ( %INTEGRATION_FS_DIRECT%, curve{$CrvName$}depvar{%ind_DepVar%}, $MaterialTag$ )

Note: In case of multiphase simulations with detection of interface connections (see PHASE_distinction), the interface points are treated like free surface points.