The function is based on a geometric series where some of input parameters can be modified in order to attempt to keep a geometric distribution.
&MESH_FUNCTION_DATA Function_Name="GEOMETRIC_SERIE_2", Number_of_Cells= 32 , Length= 1.0 , Left_Cell_Size= 2.0d-02 , Right_Cell_Size= 5.0d-02 , Reverse_Ordering= .false. /
Here, the Left_Cell_Size and Right_Cell_Size are associated to the minimum and maximum cell sizes at the tips.
The cell size distribution $h(l)$ is computed by estimation of the cell ratio in regard to the length, The Minimum cell size (Left_Cell_Size), the maximum cell size (Right_Cell_Size) and the cell number (Number_of_Cells).
The procedure is recursive and different parameters can be adjusted at each step in order to find the best compromise.
It can be relevant to check the data after computing.