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4.3.2 Pruning and Consistency Check
So far the HRLE data structure contains the updated LS values
for all grid points from the active layer
. As described in Section 3.4.2 a pruning procedure is necessary to avoid dense sets of active grid points. Again, a stencil of iterators, similar to that required for the computation of first order finite differences, is moved over the data structure. At the same time a new HRLE data structure is set up in which all changes are stored. The new HRLE data structure is constructed by copying the old one, while skipping defined grid points which do not have an opposite signed neighbor. These grid points are added to undefined runs instead.
Since the neighbors of active grid points (belonging to
) have not been updated yet, this early pruning procedure works only if the signs of nonactive grid points (
) are not altered during the entire time integration step. According to Section 3.4.2 the signs of nonactive grid points are maintained, if the CFL number
fulfills

(4.8) 
As a consequence, the presented implementation of the sparse field method only allows CFL numbers satisfying this condition.
Before a defined grid point is inserted into the new HRLE data structure, it is first checked, if its LS value is greater than
or smaller than
, while that of any neighboring defined grid point is less than
or larger than
, respectively. If this is the case, the prerequisite of the sparse field LS method (3.27) would be violated. To guarantee the robustness of the algorithm the LS value must be reduced to
(while keeping its sign) before insertion into the new HRLE data structure. After completing the iteration over the old HRLE data structure and finishing the setup of the new one, the old HRLE data structure can be deleted.
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Otmar Ertl: Numerical Methods for Topography Simulation