On sectional techniques for the solution of the breakage equation

The breakage equation is of great significance for modeling many physicochemical processes. The need for its extension to more than one internal coordinates in spatially distributed environment renders crucial the development of efficient numerical methods for its solution. In the present work two new sectional methods (Cell Average Technique and Extended Cell Average Technique) recently applied to the coagulation equation are implemented to breakage equation and tested extensively against the well-established Fixed Pivot Technique. The results of the analysis show that whereas the new methods cannot predict the complete particle size distribution better than the Fixed Pivot Technique (despite their superiority in the case of coagulation), they are very successful in predicting the moments of the distribution even for coarse grids. Thus, especially the Extended Cell Average Technique can be considered as a refinement of the moments method with increased number of degrees of freedom but also increased accuracy.