High Accuracy Numerical Methods For Chromatographic Models

Chromatography is a separation and analysis method,which has a very wide range of applications in analytical chemistry,organic chemistry,biochemistry and other fields.Numerical solution and simulation are important methods to carry out chromatographic analysis.In this thesis,several basic chromatographic models are introduced,including ideal model,equilibrium diffusion model and lumped kinetic model.The chromatographic models are mainly in the form of convection-diffusion equations or equations.The characteristics of this kind of equation is the solution which may appear in a limited time,even if the given initial value is a very smooth.For this reason,we consider discontinuous Galerkin method to solve it.Firstly,we focus on one dimensional convection-diffusion equation to consider its discontinuous Galerkin method and program implementation.And the numerical performance of the discontinuous Galerkin method for the hyperbolic conservation laws,the diffusion equation and the convection-diffusion equation is also tested.Finally,for the equilibrium diffusion model(EDM)in the nonlinear chromatographic model,the spatial discretization uses the discontinuous Galerkin method,and constructs a numerical flux applied to the scheme,and three-dimensional basis function is selected.The time discretization uses the third order TVD Runge-Kutta method and the backward Euler method respectively,in which the Newton iteration method is used to deal with the nonlinear term.In addition,a slope limiter is introduced to suppress the pseudo-oscillation caused by the convective term.The numerical results show that the proposed method is suitable for dynamic simulation of chromatographic processes.