Numerical Solution Strategies in Permeation Processes

In this work, the strategy for numerical solutions in transport processes is investigated. Permeation problems can be solved analytically or numerically by means of Finite Difference Method (FDM), while choosing Euler forward explicit backwards implicit formalism. The first method easiest and most commonly used, not yet well established needs further development. Hereafter, a possible solution Crank-Nicolson algorithm presented, which makes use matrix multiplication inversion, instead step-by-step FDM If one considers one-dimensional diffusion case, concentration elements expressed as time dependent vector, also contains boundary conditions. stable inversion performed Branch Bound (B&B) [2]. Furthermore, paper will investigate, whether larger step used speeding up simulations. stability range investigated eigenvalue estimation backward. addition, third solver considered, referred to Combined Solver, that made last two ones. Finally, [9] All these results are compared with analytical solution. analyzed Steady State Eigenvector (SSEV), mathematical entity was developed ad hoc present work. obtained Daynes [6,7].