Core-shell particles allow highly efficient and fast separation of complex samples. They provide advantages over fully porous particles, such as highly efficient separation with fast flow rate due to shorter diffusional path length in particle macropores. On the other hand, capacities are reduced due to the inert core. This work is focused on the numerical approximation of a nonlinear general rate model for fixed beds packed with core-shell particles. The model equations consider axial dispersion, interfacial mass transfer, intraparticle diffusion, and multi-component Langmuir isotherm. A semi-discrete high resolution flux-limiting finite volume scheme is proposed to accurately and efficiently solve the model equations. The scheme is second order accurate in axial and radial coordinates. The resulting system of ordinary differential equations (ODEs) are solved by using a second-order TVD Runge-Kutta method. For illustration, a few selected scenarios of single solute and multi-component elution bands are generated to study theoretically the effects of the core radius fractions on the course of elution curves. Typically applied performance criteria are evaluated for identifying ranges of optimum values of the core radius fraction. (C) 2016 Elsevier Ltd. All rights reserved.