On a high resolution Godunov method for a CFD-PBM coupled model of two-phase flow in liquid-liquid extraction columns

This paper is about the numerical solutions for a computational fluid dynamics-population balance model (CFD-PBM) coupled model of two-phase flow in a liquid-liquid extraction column. The model accounts for a complete description between both the dispersed and continuous phases, and constitutes a hyperbolic system of equations having a linearly degenerate nature. A numerical algorithm based on operator splitting approach for the numerical solution of the model is used. The homogeneous part is solved using the TVD MUSCL-Hancock scheme. Numerical results are presented, demonstrating the accuracy of the proposed methods and in particular, the accurate numerical description of the flow in the vicinity of the contact discontinuities.