%INTEGRATION_FS%

surface integration of a vector valued function along the free surface

INTEGRATION($IntInd$) = ( %INTEGRATION_FS%, Integrand_x, Integrand_y, Integrand_z, $MaterialTag$ )

This computes the integral with respect to the free surface $ \partial\Omega_\text{FS}$ identified by the material flag

\begin{align} I_\text{FS} = \int_{\partial\Omega_\text{FS}} {\bf u} \cdot {\bf n} dA \end{align}

by a sum approximation

\begin{align} I_\text{FS} \approx \sum_{i \in P_\text{FS}} ({\bf u}_i \cdot {\bf n}_i) A_i,\end{align}

where $ {\bf n}$ represents the local free surface normal. The integrand $ {\bf u}$ is given by the vector (Integrand_x, Integrand_y, Integrand_z), whose components are all of type ExpressionOfIntegrand. $ P_\text{FS}$ is the set of all boundary points with the given material flag and $ A_i$ is the area of the i-th point. The material flag $MaterialTag$ defines the integration area (analogous to the POSTPROCESS-flags for %INTEGRATION_BND%). 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($pressure_x$) = ( %INTEGRATION_FS%, [Y%ind_p%+Y%ind_p_dyn%], [0], [0], $MaterialTag$ )

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