Numerical study for two models in chromatography using modified Rusanov scheme.

This article focuses on developing and validating a modified Rusanov (mR) numerical scheme to solve nonlinear chromatographic models that describe the separation of chemical components in fluid mixtures. Two nonlinear chromatography systems are examined, and the mR method—characterized by a predictor-corrector approach with a locally controlled diffusion parameter—is constructed and compared against classical Rusanov and Lax–Friedrichs schemes through five test cases for each model. Numerical results demonstrate that the mR scheme achieves higher accuracy and better shock resolution without nonphysical oscillations, effectively capturing rarefaction waves, shocks, and delta shocks. The study concludes that the mR method is a reliable and efficient tool for simulating chromatographic processes governed by conservation laws in applied sciences.