화학공학소재연구정보센터
Chemical Engineering Communications, Vol.139, 159-200, 1995
Application of Petrov-Galerkin Finite-Element Method to Nonlinear Transient Diffusion-Convection-Reaction System
Streamline upwind Petrov-Galerkin finite element method (SUPG FEM) was considered to solve for the general chemically reactive flow system with convection, diffusion, and reaction. A nonlinear transient pseudo-homogeneous catalytic reactor model with Dankwert boundary conditions in two-dimensional domain was selected as an numerical example. The effect of velocity distribution on the dynamics of the system and the wrong way behavior was discussed in detail and the dependence of the steady-state solution upon a set of dimensionless parameters was investigated. In addition, for the numerical test of the discontinuity capturing scheme, the one-dimensional pseudo-homogeneous plug Bow reactor model which incudes a discontinuity by a high convection and reaction rate was considered and the SUPG FEM was applied to solve for the model equation. The results from the SUPGFEM were then compared with the theoretical result from the method of characteristics and also with those from various formula based on the streamline upwind biased finite difference method (SUPG FDM). Both the SUPG FEM and the SUB FDM were found to be the effective numerical techniques for capturing the discontinuity of the convective flow system and reducing the numerical oscillations.