Current numerical solutions of population balance problems including growth are limited by
the Courant condition time step constraint. As a result, particle size ranges must be restricted
and limited growth rate mechanisms can be solved. A thorough analysis of growth rate
mechanisms and dynamics is presented that relates the growth rate mechanisms and particle
size ranges to the time step limit. These relationships reveal a method for producing the optimal
time step for any growth rate model, which can increase the time step by a factor of 107. When
these methods are combined with previous approaches, new hybrid methods are developed that
allow the user to flexibly choose the optimal time step given the resolution requirements of the
problem, producing solutions that are 104−107 times faster than conventional solutions. The
numerical accuracy of these solutions compares favorably against analytical solutions, demonstrating their applicability across a wide range of problems.