%INTEGRATION_ABSFLUX%

flux integration of a functional by counting the MESHFREE points that slip over a given control surface independent of the direction

begin_alias{} "AliasOmega" = " ... IDENT%IDENT_BlindAndEmpty% ... POSTPROCESS$PostprocessTag$ ... " # definition of AliasOmega end_alias INTEGRATION($IntInd$) = ( %INTEGRATION_ABSFLUX%, ExpressionOfIntegrand, $PostprocessTag$ )

Warning: %INTEGRATION_ABSFLUX% as well as %INTEGRATION_ABSFLUX_TIME% work only for boundary elements marked with %IDENT_BlindAndEmpty% . It computes the flux of a functional $ f$ (ExpressionOfIntegrand) across a control surface in the sense:

\begin{align} I_\text{AbsFlux} = \int\limits_{\partial\Omega} f \cdot \left|{\bf v}^T {\bf n}\right| dA\end{align}

This integral is approximated by summing up the MESHFREE points which are currently penetrating through the control surface $ \partial\Omega$:

\begin{align} I_\text{AbsFlux} \approx \sum_{i \in P_\text{slipped}} f_i \cdot \frac{V_i}{\Delta t}\end{align}

$ P_\text{slipped}$ is the set of all MESHFREE points which slipped over $ \partial\Omega$ in this time step. Here, the direction of penetration of a MESHFREE point does not matter. For representative mass measurements, see also RepresentativeMassAlgorithm.

Note: Skip is not recommended for this type of integration statement.