Application of a space-time CE/SE (Conservation Element Solution Element) method to the numerical solution of chromatographic separation processes

For solving partial differential equations (or distributed dynamic systems), the method of lines (MOL) and the space-time conservation element and solution element (CE/SE) method are compared in terms of computational efficiency, solution accuracy and stability. Several representative examples including convection-diffusion-reaction PDEs are numerically solved using the two methods on the same spatial grid. Even though the CE/SE method uses a simple stencil structure and is developed on a simple mathematical basis (i.e., Gauss' divergence theorem), accurate and computationally-efficient solutions are obtained in a stable manner in most cases. However, a remedy is still needed for PDEs with a stiff source term. It seems to be out of date to use the MOL for solving PDEs containing steep moving fronts because of the dissipation error caused by spatial discretization and time consuming computations. It is concluded that the CE/SE method is adequate to capturing shocks in PDEs but for diffusion-dominated stiff PDEs, the MOL with an ODE time integrator is complementary to the CE/SE method.