Numerical study for two models in chromatography using modified Rusanov scheme

Abstract

We investigate the conservation laws that explain the chemistry process of isolating a single component from a mixture using column chromatography. We construct the modified Rusanov (mR) technique to solve the chromatography system. This technique is divided into two parts, the first of which is reliant on a local parameter which enables diffusion control. The conservation equation is recovered in stage two. It is crucial to make sure the numerical approach is built in a way that it is conservative on the overlap and, additionally, that the approximative solutions converge to the weak solution. This strategy is clear-cut, not difficult to use and precise. We compare the mR scheme via the Rusanov scheme and Lax–Friedrichs scheme via five test cases. This numerical research validates the mR scheme's efficacy. Finally, the mR approach can be utilized to solve a variety of conservation laws arising in natural science.