## Abstract

For solving partial differential algebraic equations (PDAEs), the space-time conservation element/solution element (CE/SE) method is addressed in this study. The method of lines (MOL) using an implicit time integrator is compared with the CE/SE method in terms of computational efficiency, solution accuracy and stability. The space-time CE/SE method is successfully implemented to solve PDAE systems through combining an iteration procedure for nonlinear algebraic equations. For illustration, chromatographic adsorption problems including convection, diffusion and reaction terms with a linear or nonlinear adsorption isotherm are solved by the two methods.

The CE/SE method enforces both local and global flux conservation in space and time, and uses a simple stencil structure (two points at the previous time level and one point at the present time level). Thus, accurate and computationally-efficient numerical solutions are obtained. Stable solutions are guaranteed if the Courant-Friedrichs-Lewy (CFL) condition is satisfied. Solutions to two case studies demonstrate that the CE/SE numerical solutions are comparative in accuracy to those obtained from a MOL discretized by the 5th-order weighted essentially non-oscillatory (WENO) upwinding scheme with a significantly shorter calculation time. (C) 2003 Elsevier Ltd. All rights reserved.

The CE/SE method enforces both local and global flux conservation in space and time, and uses a simple stencil structure (two points at the previous time level and one point at the present time level). Thus, accurate and computationally-efficient numerical solutions are obtained. Stable solutions are guaranteed if the Courant-Friedrichs-Lewy (CFL) condition is satisfied. Solutions to two case studies demonstrate that the CE/SE numerical solutions are comparative in accuracy to those obtained from a MOL discretized by the 5th-order weighted essentially non-oscillatory (WENO) upwinding scheme with a significantly shorter calculation time. (C) 2003 Elsevier Ltd. All rights reserved.

Original language | English |
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Journal | Computers & Chemical Engineering |

Volume | 28 |

Issue number | 8 |

Pages (from-to) | 1309-1324 |

ISSN | 0098-1354 |

DOIs | |

Publication status | Published - 2004 |