A concentration-preserving discontinuous Galerkin method for multi-component preparative chromatography

Multi-component liquid chromatography mass balance equations are typically formulated as time-dependent, nonlinear, convection-dominated partial differential equations (PDEs). In this study, we develop, analyze, and numerically validate a concentration-preserving discontinuous Galerkin (DG) method for solving equilibrium-dispersive preparative chromatography with a model-free adsorption isotherm. The proposed semi-discrete DG scheme is proven to conserve the concentrations of all species and to achieve optimal L2 error estimates. For the temporal discretization, we adopt a third-order total variation diminishing (TVD) Runge-Kutta method, combined with the minmod limiter to effectively control nonphysical oscillations and preserve monotonicity, especially near steep gradients or discontinuities. Numerical experiments confirm the effectiveness of the solver in handling nonlinear chromatography PDEs with complex adsorption isotherms and demonstrate optimal convergence rates for the resulting numerical solutions.