SequentialFiltering
generate writeout to timestep files due to simple sequential filters
In many cases, the user wishes to reduce the data produced by the .timestep files. If
INTEGRATION data are explicitly written to
a dedicated .timestep file by the
begin_timestepfile{-clause, then one can define time filters.
Example: additinal sequential filtering
Over a number of time cycles, the filtered integration results are averaged by the following way:
\begin{align} u^{integ}_{average} = \frac{1}{2} \frac{ \sum \limits_{i \in N} (u^{integ}_i+u^{integ}_{i-1})(t_i-t_{i-1})}{ \sum \limits_{i \in N} (t_i-t_{i-1})}\end{align}
that means it is a weighted average with the time step size to be the weight. In this way, we can guarantee conservation properties of some variables like momentum etc.