Solution of coupled nonlinear hyperbolic type aggregation-breakage models with two-dimensional extension

Aggregation and collision-induced breakage equation have important applications in different branches of science and day to day life. Processes such as twin-screw wet granulation, bubble growth, rennet induced aggregation in dairy process, raindrop formation etc. can be modeled using physically relevant kernels. These kernels are mostly represented by more complex mathematical terms, often resulting in the underlying physics of the system becoming more complex. In this article, semi-analytical homotopy analysis method (HAM) is designed and employed and compared with finite volume method (FVM) [Das and Saha (2024), Z Angew Math Phys 75:125] to understand the dynamical behavior of the one-dimensional aggregation and collision-induced breakage equation and assess the accuracy as well as efficiency of the proposed techniques. Further, we propose the extension of FVM and HAM for the two-dimensional case and execute with numerical examples. A thorough investigation suggests that FVM is computationally expensive and requires additional attention to preserve particle properties. On the other hand, the semi-analytical method incorporates an auxiliary parameter that adjusts and controls the convergence region, ensuring highly accurate results with rapid convergence. The results demonstrate that the semi-analytical method is more robust and versatile compared to FVM.