An insight into discrete and accelerated decomposition techniques for improved accuracy of multi-dimensional hyperbolic aggregation model arising in bubble column

We present and analyze new solution techniques for the hyperbolic nonlinear aggregation equation involving physical phenomena like bubble growth in a column, raindrop formation. The decomposition method is designed to generate the solution. We also extend the model for solving problems in multi-dimensional setup. Mathematical stability and convergence analysis of new scheme is performed using contraction mapping principle. Accuracy and efficiency of the time dependent solutions are further accelerated and stabilized for longer times by coupling the solutions obtained from analytical method with the Padé approximation technique. Reliability of the coupled approach is validated by considering several test problems. Validation of the proposed technique is performed by modifying the classical finite volume method [Bourgade and Filbet, Math. Comp. 77(262), 851–882 (2008)] by introducing weight factors. We also present this weighted scheme for multidimensional hyperbolic aggregation equation. Qualitative and quantitative comparison of significant physical entities like particle size distribution, total mass, number and average size are carried out with respect to exact values. In several occasions the coupled decomposition and Padé technique proved to give highly accurate prediction of different physical properties as compared to the classical domain discretization techniques. Scheme based on decomposition is mathematically simple, and independent of domain discretization. When coupled with Computational fluid dynamics, this stability of solution helps in preventing divergence, errors in particle properties under complex conditions.