The Study On Numertical Method For Non-Linear Multi-Component Chromatography

Chromatographer is a new separation and analytical technique which has been developed recently. It has extensive application in many fields in practice and science experiment. Generally, the mathematical models of chromatography are initial boundary value problems of hyperbolic conservation laws in differential equation. It is very significant to study these problems not only in practice but also in theory. In general, because most chromatography is multi-component chromatography, the study in this field focuses on non-linear multi-component chromatography.In this paper, firstly, based on practical problems in chromatography, the mathematical models of non-linear multi-component chromatography are discussed. Because the model of non-linear two-component chromatography can be extended easily to multi-component chromatography, we focus on the two-component chromatographic models in this paper. Generally, this kind of models needs solving numerically. Because the solutions of the mathematical models can often display a moving steep front or even discontinuity, the tradition methods are difficult to simulate the solution accurately. For such a model, an adaptive semi-implicit upwind difference scheme is constructed. The criterion of spatial adaptation is based on a proper combination of the magnitude of the second spatial derivative and that of the first derivative of solution. We can get the node placement by solving an ordinary differential equation. Then a non-linear two-component chromatographic model in article [1] is simulated by the new algorithm and the numerical result is compared with that by the corresponding algorithm with equal step. The results indicated that the new algorithm can simulate the models better.