Discretization of the Size Coordinate
To solve the population balance equation, the size parameter is discretized into smaller size intervals. The interface provides three different options for discretization of the internal coordinate, linear discretization, geometric discretization, and logarithmic discretization. Linear discretization divides the size coordinate into evenly sized intervals. The size at the end of interval i is calculated according to
(3-153)
and
(3-154)
where I is the total number of intervals and LI and L0 are the largest and smallest size solved for respectively.
Geometric discretization instead results in intervals with an increasing interval length as the size coordinate increases. This takes the form
(3-155)
and where an additional point Lmin, only used for discretization is defined as (Ref. 1)
(3-156)
The last option, logarithmic discretization gives a discretization on the form
(3-157)
Further on, we will not only see the size at the right-hand boundary of the interval, Li, being used for calculating growth and dissolution rates but also the size at the center of the interval, denoted Lmid,i, being used for calculating aggregation and breakage contributions. Lmid,i is taken as the size at the exact mid point of the interval as
(3-158)