The full multicomponent population dynamic equation is developed for systems with coagulation and solved using the split composition distribution method. A full discussion of the origins of this method and its advantages over conventional methods is followed by a complete and rigorous explanation of its numerical implementation. The Wiener expansion is introduced as a method for representing compositional variation in a number density distribution that is solved by orthogonal collocation on finite elements. Results are obtained by numerical integration using fifth-order Runge-Kutta and favorably compared to analytical results.

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.