A novel partial differential algebraic equation (PDAE) solver: Iterative space-time conservation element/solution element (CE/SE) method

  • Lim Y
  • Chang S
  • Jørgensen S
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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. © 2003 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Chromatographic adsorption problem
  • Method of lines (MOL)
  • Numerical analysis
  • Partial differential algebraic equations (PDAEs)
  • Protein ion-exchange separation
  • Space-time CE/SE method

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