Comparison and Analysis of Three Methods for Numerical Solution of Droplet Breakage Equation

Three methods for numerical solution of droplet breakage equation(PBE) under the population balance concept in batch system are introduced: fixed pivot technique(FPT), method developed by Attarakih(MDA), cell averaged technique(CAT). Differences and accuracies are also discussed. For overcoming the significant deviation of number density in the left boundary of FPT, a slight modification is recommended, and the numerical results show good agreement with analytical solution. All of numerical solutions for differential equations set are approached by fourth-order Runge-Kutta method, and the algorithms are programmed by C programming language. The numerical results show that the FPT and MDA have almost the same accuracy under large interval width, while the CAT is of better accuracy and efficiency, which show a prosperous future in solving the simultaneous breakage and aggregation equations. However, all of the three methods show steady and solid results even after a relatively long processing time.