Simulating the models of Tsikkou and Wang via mR scheme in chromatography

We investigate two systems of conservation laws that explain the chemistry process of isolating a single component from a mixture using column chromatography. We design the modified Rusanov (mR) approach for solving these chromatography models. This approach is separated into two phases, the first of which is controlled by a local parameter. The conservation equation is recovered in stage two. This tactic is unambiguous, simple to use, and accurate. Through several test cases, we compare the mR scheme to the Rusanov system and the Lax-Friedrichs scheme. According to the numerical simulation, the proposed mR technique has a high resolution and provides precise simulations for the two chromatographic models with strong shocks and rarefaction. Finally, the mR approach can be utilized to solve a variety of other applicable scientific models.